Download triangle sum theorem word problems

GEOMETRY WORKSHEET Triangle sum theorem
1. In ΔPQR, the measure of  P is 36°. The measure of  Q is five times the measure of  R. Find
the measure of  Q and  R.
2. The measure of an exterior angle of a triangle is 120°. The interior angles that are not adjacent
to this exterior angle are congruent. Find the measures of the interior angles of the triangle.
3. You want to make a wooden billiard rack. The rack will be an equilateral triangle whose side
length is 33.5 centimeters. You have a strip of wood that is 100 centimeters long. Do you need
more wood? Explain.
4. You are bending a wire to make a coat hanger. The length of the wire is 88 centimeters, and 20
centimeters are needed to make the hook portion of the hanger. The triangular portion of the
hanger is an isosceles triangle. The length of one leg of this triangle is 3/5 the length of the base.
Sketch the hanger. Give the dimensions of the triangular portion.
5. The lengths of two legs of an isosceles triangle are represented by the expressions (2x – 5) and
(x + 7). The perimeter of the triangle is 50 cm. Find the length of the base of the triangle.
6. Which of the terms below can be used to describe a triangle with two 45° interior angles?
a) acute
b) right
c) scalene
d) obtuse
7. The ratio of the three angles of a triangle is 3:4:5. Find the measure of each angle. Classify the
triangle by its angles.
8. The ratio of the three angles of a triangle is 4:6:8. Find the measure of each angle. Classify the
triangle by its angles.
9. One acute angle of a right triangle is 2/3 the measure of the other acute angle. What is the
measure of the two acute angles?
10. Find the value of x in the diagram.
(2x + 4)°
(2x – 9)°
(x)°
G
D
F
11. Given: ⃗⃗⃗⃗⃗
𝐴𝐷 bisects  FAC
Find:  BGD
64°
E
60°
A
̅̅̅̅ ll 𝐴𝐷
̅̅̅̅, 𝐹𝐵
̅̅̅̅ ll 𝐸𝐷
̅̅̅̅,  1 =  2
12. Given:  GFB = 110°, 𝐺𝐹
Find:  3.
70°
C
B
H
G
E
F
1
A
B
C
3
2
D
13. Find the measure of each angle of a triangle whose exterior angles, one at each vertex, have the
measures 2x + 10, x + 20, and x + 30.