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Unit IV A Quiz Review
Unit IV A Quiz Topics: Lessons 5-1 Lines, 5-3 Angles of Triangles, 5-4 Polygons and Angles,
5-5 The Pythagorean Theorem, 5-6 Use The Pythagorean Theorem, 5-7 Distance on the Coordinate Plane
Circle the letter for the correct answer in the blank at the right of each question.
1. What is the value of x in the figure at the right?
A.
50
B.
62
C.
68
D. 112
2. Which pair of angles is not congruent?
F. ∠1 and ∠8
H. ∠4 and ∠7
G. ∠3 and ∠5
I. ∠2 and ∠5
5 6
8
7
4 3
1
2
3. In the figure below, m∠1 = x and m∠2 = x – 8. Which statement could be used to
prove that x = 49?
A. m∠1 = m∠2
B. m∠2 = 49°
1
2
3
C. m∠1 + m∠2 = 90°
D. m∠1 + m∠2 = 180°
4. Coty painted a right triangle on paper. The hypotenuse of his triangle is 18 inches and one of the legs is 7 inches.
What is the length of the third side? Round to the nearest tenth if necessary.
F. 19.3 in.
G. 16.6
in.
H. 14.2 in.
I. 11 in.
5. What is the measure of an exterior angle of a regular octagon?
A. 72⁰
C. 45⁰
B. 60⁰
D. 40⁰
6. In the figure at the right, find the m∠5 if m∠3 = 115°.
2x°
7. What is the value of x in the triangle below?
25°
25°
8. Find the sum of the measures of the interior angles of an 18-gon.
220 ft
9. In the diagram, Caito is flying his kite. Write and solve an equation to find
how far above Caito’s head the kite is. Round your answer to the nearest
tenth if necessary.
x ft
200 ft
10. The Pentagon building in Washington, D.C., is named because it is in the shape of a regular pentagon.
What is the sum of the measures of its interior angles?
11. Davey’s log cabin is in the shape of a rectangle. Its dimensions are 40 feet by 24 feet. Find the length of
the diagonal of the floor of the cabin. Round your answer to the nearest tenth if necessary.
12. Find the distance between points P(3, ) and Q(7, 4). Round to the nearest tenth if necessary.
For Exercises 1 and 2, write and solve an equation to find each missing length.
Round to the nearest tenth if necessary.
1. An observer is standing 20 feet from a tree with a hanging birdhouse. She is looking at
the birdhouse. How far from the ground is the birdhouse? Round to the nearest tenth if
necessary.
25 ft
20 ft
x
2. Kenneth wants to wrap a collapsible fishing rod in the box shown at the right. Find the
length of the diagonal of the box. Round to the nearest tenth if necessary.
For Exercises 3 and 4, find the distance between each pair of points with the given coordinates.
Round to the nearest tenth if necessary.
3. (4.25, 5.5), (3.5, 0)
4. (2, 4), (5, 2)
Find the value of x in each figure.
5.
6.
7. A shelf is in the shape of a triangle. Find the angles of the triangle if the measures of the angles are in the ratio
x : x : 4x.
8. What is always true about angles in an equilateral triangle?
9. What is the perimeter of the triangle?
10. Find the measure of an exterior angle of a regular decagon.
11. Find the sum of the measures of the interior angles of a 50-gon.
12. The side view of a house (the “side elevation”) is often in the shape of a pentagon. If the angle at the roof
is 150° and there are two other angles of 90°, what is the sum of the measures of the other two angles?
13. A triangle has side lengths of 10 inches, 24 inches, and 26 inches. Is the triangle a right triangle? Explain.
Unit IV A Quiz Review Solutions
Unit IV A Quiz Review Solutions
Unit IV A Quiz Review Solutions
Unit IV A Quiz Review Solutions