Name: ___________________________________
Geometry-A
Applications of the Triangle Angle-Sum Theorem
1. The measures of the three angles of a triangle are in the
ratio 3: 4: 5. Find the measure of the largest angle.
A
80
E
2. If one of the angles of a triangle is 80, find the
measure of the angle formed by the bisectors of the
other two angles.
B
C
D
3. Given: m1  150 , and the measure of mD is twice
that of mE .
Find the measure of each angle of the triangle.
1
E
F
B
40
4. Given: Diagram as marked.
Find: mB
A
C
7
6
5
5. Given: m1  130 ; m7  70
Find the measures of the remaining angles.
3
2
1
4
G
50
6. If one of the angles of a triangle is 50, find the
measure of the angle formed by the bisectors of the
other two angles.
M
H
J
O
7. Given: mQRS  (4 x  6) ; mP  (x  24) ; and
mO  (2 x  4)
Find: mO
S
P
R
8. In DEF , the sum of the measures of D and E is
110. The sum of the measures of E and F is
150. Find the sum of the measures of D and F .
9. The measures of two angles of a triangle are in the ratio
of 2:3. If the third angle is 4 degrees larger than the
larger of the other two angles, find the measure of an
exterior angle at the third vertex.
P
10. Given: mPST  ( x  3 y ) ; mP  45 ;
mR  (2 y ) ; mPSR  (5 x)
Find: mPST
T
R
S
NOTES:
1
Triangle Angle-Sum Theorem: The sum of the
measures of the angles of a triangle is 180.
m1  m2  m3  180
Triangle Exterior Angle Theorem: The
measure of each exterior angle of a triangle equals
the sum of the measures of its two remote interior
angles. 4 is an exterior angle; the remote
interior angles in relation to 4 are 1 and 2 .
m4  m1  m2
Additional Theorems About Parallel and
Perpendicular Lines:
If two lines are parallel to the same line, then they
are parallel to each other. If a||c and b||c then
a||b.
In a plane, if two lines are perpendicular to the
same line then they are parallel to each other. If
m is perpendicular to t and n perpendicular to t,
then m||n.
4
3
2