Question

The figure is not drawn to scale.

If m<2=39 and m<3=30, what is m<1?
A)111
B)86
C)71
D)69

Answer 1

D

Explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠1 is an exterior angle, thus

∠1 = ∠2 + ∠3 = 39 + 30 = 69° → D

Answer 2

○ 69°

Explanation:

Since you have two angle measures defined, use the Triangular Interior Angles Theorem to find the third angles measure:

`180° = m∠3 + m∠2 + m∠1`

180° = 30° + 39° + m∠4

|________|

180° = 69° + m∠4

-69° - 69°

__________________

111° = m∠4

Then, since m∠4 forms a linear pair with m∠1, use the Supplementary Angles Theorem:

`180° = 111° + m∠1`

- 111° - 111°

________________________

69° = m∠1

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