EXTERIOR ANGLE THEOREM TRIANGLE WORKSHEET

Find the missing values of the following.

Problem 1 :

Solve for x.

Solution

Problem 2 :

Solve for x and find m ∠A.

Solution

Problem 3 :

Solve for x and find m ∠B.

Solution

Problem 4 :

Solve for x.

Solution

Problem 5 :

Solve for x.

Solution

Problem 6 :

Solve for x, find m ∠ A.

Solution

Problem 7 :

Solve for x.

Solution

Problem 8 :

Describe and correct the error in finding m∠1.

Solution

Problem 9 :

Describe and correct the error in finding m∠1.

Solution

Problem 10 :

The measure of one of the base angles of an isosceles triangle is 42°. The measure of an exterior angle at the vertex of the triangle is

1) 42°        2) 84°         3) 96°       4) 138°

Solution

The variable expression represent the angle measures of a triangle. Find the measures of each angle. Then classify the triangle by its angles.

Problem 1 :

∠A = x°, ∠B = 2x°, ∠C = (2x + 15)°

Solution

Problem 2 :

∠A = x°, ∠B = 7x°, ∠C = x

Solution

Problem 3 :

∠A = (x - 15)°, ∠B = (2x - 165)°, ∠C = 90°

Solution

Find the measure of the exterior angle shown.

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

Problem 7 :

In triangle PQR, the measure of ∠P is 36. The measure of ∠Q is five times the measure of ∠R. Find ∠Q and ∠R.

Solution

Problem 8 :

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.

Solution

Problem 9 :

The angles of a triangle have measures of 2(5𝑥 − 3), 3(𝑥 + 5), and 8𝑥 + 3. Determine the sum of the largest and smallest angle.

Solution

Problem 10 :

Two angles of a triangle have equal measures, but the third angle's measure is 36° less than the sum of the other two. Find the measure of each angle of the triangle.

Solution

Find the values of the variables :

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Problem 5 :

Solution

Problem 6 :

Solution

Problem 7 :

Two angles of a triangle have equal measures, but the third angle's measure is 36° less than the sum of the other two. Find the measure of each angle of the triangle.

Solution

Problem 8 :

Find the measures of the angles of an isosceles triangle if the measure of the vertex angle is 40 degrees less than the sum of the measures of the base angles.

Solution

Problem 9 :

In a triangle ABC, ∠A = 2x + 7, ∠B = 5x - 15, and ∠C = 6x. What is the value of x and what are the measures of angles A, B, and C?

Solution

Problem 10 :

In a triangle XYZ, ∠X = 37°, ∠Y = 45°, and ∠Z = 3x + 6. What is the value of x and what is the measure of ∠Z?

Solution

Problem 11 :

Find the angle measures of a triangle if the second angle measures 10 degrees less than twice the first, and the third angle measures 25 degrees more than the second.

Solution

Find, giving reasons, the value of x:

Problem 1 :

Solution

Problem 2 :

Solution

Problem 3 :

Solution

Problem 4 :

Solution

Find the values of the variables in the following diagrams:

Problem 5 :

Solution

Problem 6 :

Solution

Problem 7 :

Solution

Problem 8 :

Solution

Problem 9 :

Solution

Problem 10 :

Solution

Problem 11 :

Solution

Problem 12 :

In FGH, m∠F = 42 and an exterior angle at vertex H has a measure of 104. What is m∠G?

1) 34    2) 62      3) 76     4) 146

Solution

Problem 13 :

In the diagram below of ABC, side BC is extended to point D, m∠A = x, m∠B = 2x + 15, and m∠ACD = 5x + 5.

What is m∠B?

1) 5       2) 20        3) 25      4) 55

Solution

Problem 14 :

In ABC shown below, side AC is extended to point D with m∠DAB = (180 − 3x)°, m∠B = (6x − 40)°, and m∠C = (x + 20)°.

What is m∠BAC?

1) 20º      2) 40º     3) 60º      4) 80º

Solution

Problem 15 :

In the diagram below of ABC, BC is extended to D

If m∠A = x² − 6x, m∠B = 2x − 3, and m∠ACD = 9x + 27, what is the value of x?

1) 10     2) 2     3) 3     4) 15

Solution