Angle Facts Exam Questions
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Angle Facts Exam Questions The diagram shows a triangle ABC. = 20º. D is a point on AB such that DB = DA = DC. Angle ABC Work out the size of angle ACB. You must show your working. ......................................................................................... ............................................................ ......................................................................................... ............................................................ ......................................................................................... ............................................................ ......................................................................................... ............................................................ Answer ......................................................... degrees (3 marks) _______________________________________________________________________________ (a)ABCD is a quadrilateral. Work out the size of the exterior angle a. ......................................................................................... ................................................... ......................................................................................... ................................................... ......................................................................................... ................................................... Answer ......................................................... degrees (3 marks) (b) Tim says he can draw a quadrilateral with exactly three right angles. Explain why this is not possible. ......................................................................................... ................................................... ......................................................................................... ................................................... ......................................................................................... ................................................... ......................................................................................... ................................................... ......................................................................................... ................................................... ......................................................................................... ................................................... (2 marks) _______________________________________________________________________________ ABC is an isosceles triangle. Triangle ABD has a right angle at B. Angle ADB = 40º Angle CBE = 50º Work out the size of angle x. ......................................................................................... ................................................... ......................................................................................... ................................................... ......................................................................................... ................................................... ......................................................................................... ................................................... Answer ......................................................... degrees (3 marks) ABC is an isosceles triangle. AB = BC Work out the values of x and y. ......................................................................................... ............................................................ ......................................................................................... ............................................................ ......................................................................................... ............................................................ Answer x = ........................................... degrees y= ...................................... degrees (3 marks) _______________________________________________________________________________ (a) Work out the size of angles a and b. ............................................................................................................................. ................... ................................................................................................................................................ ............................................................................................................................. ................... Answer a = ............................ degrees, b = ............................ degrees (3 marks) (b) Show that x + y + z = 180 ............................................................................................................................. ................... ................................................................................................................................................ ................................................................................................................................................ ............................................................................................................................. ................... (2 marks) ______________________________________________________________________________________________ ABC is a right-angled triangle. Work out the value of x. .......................................................................................................................................................... .......................................................................................................................................................... Answer x = ................................................... degrees (2 marks) ABCDE is a regular pentagon. Work out the value of x. .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... Answer x = ................................................... degrees (4 marks) ______________________________________________________________________________ ABC is an isosceles triangle. BCDE is a kite. Work out the value of x. .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... .......................................................................................................................................................... Answer ......................................................... degrees (3 marks) _______________________________________________________________________________ (a) ABCD is a quadrilateral. The side DC is extended to E. Work out the value of x. ................................................................................................................................................ ................................................................................................................................................ Answer ........................................................... degrees (3 marks) (b) Calculate the size of the exterior angle of a regular hexagon. ................................................................................................................................................ ................................................................................................................................................ ................................................................................................................................................ Answer ........................................................... degrees (2 marks) The diagram shows a regular octagon. Calculate the size of the exterior angle of the regular octagon, marked y on the diagram. ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………(2 marks) ________________________________________________________________________________ In the diagram AB is parallel to CD. Work out the value of x. ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… ……………………………………………… …………………………………..(3 marks) ______________________________________________________________________________ In the diagram, AB is parallel to CD. (a) State the value of x. Give a reason for your answer. Answer ..................................................................... degrees Reason .................................................................................................................................. ................................................................................................................................................ (2 marks) (b) Find the value of y. ................................................................................................................................................ ................................................................................................................................................ Answer .......................................................... degrees (2 marks) ______________________________________________________________________________ ABCD is a rhombus and ABCE is a kite. Work out the value of x. ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………………………… ………………………………………(4 marks)
