**Finding missing angle measures in triangles worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on finding missing angle measure in triangles.

1. Find the missing angle measure in the triangle given below.

2. Find the missing angle measure in the triangle given below.

3. Find the missing angle measure in the triangle given below.

4. Find the measure of each angle in the triangle given below.

**Problem 1 :**

Find the missing angle measure in the triangle given below.

**Solution :**

**Step 1 :**

Write the Triangle Sum Theorem for this triangle.

m∠A + m∠B + m∠C = 180°

**Step 2 :**

Substitute the given angle measures.

55° + m∠B + 100° = 180°

Simplify.

m∠B + 150° = 180°

Subtract 150° from both sides.

aaaaaaaaaaaaaaaaa m∠B + 150° = 180° aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa - 150° - 150° aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa ----------------------- aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa m∠B = 30° aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa ----------------------- aaaaaaaaaaaaaaa

Hence, m∠B = 30°

**Problem 2 :**

Find the missing angle measure in the triangle given below.

**Solution :**

**Step 1 :**

Write the Triangle Sum Theorem for this triangle.

m∠R + m∠S + m∠T = 180°

**Step 2 :**

Substitute the given angle measures.

m∠B + 29° + 61° = 180°

Simplify.

m∠B + 90° = 180°

Subtract 90° from both sides.

aaaaaaaaaaaaaaaaa m∠R + 90° = 180° aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa - 90° - 90° aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa ----------------------- aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa m∠R = 90° aaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa ----------------------- aaaaaaaaaaaaaaa

Hence, m∠R = 90°

**Problem 3 :**

Find the missing angle measure in the triangle given below.

**Solution :**

**Step 1 :**

Write the Triangle Sum Theorem for this triangle.

m∠J + m∠K + m∠L = 180°

**Step 2 :**

Substitute the given angle measures.

71° + m∠K + 56° = 180°

Simplify.

m∠K + 127° = 180°

Subtract 127° from both sides.

aaaaaaaaaaaaaaaaa m∠K + 127° = 180° aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa - 127° - 127° aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa ----------------------- aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa m∠K = 53° aaaaaaaaaaaaaaa aaaaaaaaaaaaaaaa ----------------------- aaaaaaaaaaaaaaa

Hence, m∠K = 53°

**Problem 4 : **

Find the measure of each angle in the triangle given below.

**Solution :**

**Step 1 :**

Write the Triangle Sum Theorem for this triangle.

m∠T + m∠U + m∠V = 180°

**Step 2 :**

Substitute the given angle measures.

(7x + 4)° + (2x + 5)° + (5x + 3)° = 180°

Simplify.

14x + 12 = 180

Subtract 12° from both sides.

aaaaaaaaaaaaaaaaa 14x + 12 = 180 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa - 12 - 12 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa ----------------- aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa 14x = 168 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa ----------------- aaaaaaaaaaaaaaaaaaa

Divide both sides by 14.

14x/14 = 168/14

x = 12

**Step 3 :**

Plug x = 12 in the given angle measures.

m∠T = (7x + 4)° = (7 · 12 + 4)° = 88°

m∠U = (2x + 5)° = (2 · 12 + 5)° = 29°

m∠V = (5x + 3)° = (5 · 12 + 3)° = 63°

Hence,

m∠T = 88°

m∠U = 29°

m∠V = 63°

After having gone through the stuff given above, we hope that the students would have understood "Finding missing angle measures in triangles worksheet".

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