FINDING MISSING ANGLE MEASURES IN TRIANGLES

If we know the measures of two angles in a triangle, we can use the Triangle Sum Theorem to find the measure of the third angle.

Example 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 + 155°  =  180°

Subtract 155° from both sides.

m∠B  =  25°

Example 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∠R + 29° + 61°  =  180°

Simplify.

m∠R + 90°  =  180°

Subtract 90° from both sides.

m∠R  =  90°

Example 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. 

m∠K  =  53°

Example 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.

14x  =  168

Divide both sides by 14.

14x/14  =  168/14

x  =  12

Step 3 :

Substitute 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°

So, 

m∠T  =  88°

m∠U  =  29°

m∠V  =  63°

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