Question

Find the value of x. m<2= x + 119
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Answer 1

x = -10

Explanation:

Find the measure of angle m∠2

The triangles are isosceles triangles, the base angles are equal.

The other base angle is also 64°.

Using Triangle Sum Theorem.

64 + 64 + y = 180

y = 52

The top angle is 52°.

The whole angle is 90°.

90 - 52 = 38

The second triangle has base angles equal.

Using Triangle Sum Theorem.

38 + z + z = 180

z = 71

The two base angles are 71°.

Angles on a straight line add up to 180°.

71 + m∠2 = 180

m∠2 = 109

The measure of m∠2 is 109°

Find the value of x

m∠2 = x + 119

109 = x + 119

x = 109 - 119

x = -10

Answer 2

Answer: x = -10

Explanation:

see image

A) congruent sides implies congruent angles A = 64°

B) Use the Triangle Sum Theorem: 64° + 64° + B = 180° --> B = 52°

C) B and C are complimentary angles: 52° + C = 90° --> C = 38°

D) Use the Triangle Sum Theorem knowing that congruent sides implies congruent angles: 38° + 2D = 180° --> D = 71°

∠2) D and ∠2 are supplementary angles: 71° + ∠2 = 180° --> ∠2 = 109°

Solve for x:

109° = x + 119

-10 = x