Given that < 1 and < 2 are supplementary angles and that m< 1=115 degrees, explain how to find the measure of the complement of < 2

25°

Step-by-step explanation:

Calculate the supplement of ∠1.  

Two angles are supplementary when they add up to 180°.

∠1 + ∠2 = 180°

         ∠1 =115°     Substitute the value

115 + ∠2 = 180    Subtract 115 from each side

        ∠2 = 65°

Calculate the complement of ∠2

Let ∠3 be the complement of ∠2.

Two angles are complementary when they add up to 90°.

∠2 + ∠3 = 90°     Substitute m∠2

65 + ∠ 3 = 90      Subtract 65 from each side

        ∠3 = 25°

The measure of the complement of ∠2 is 25°.

You can find the measure of the complement of <2 by using the linear pair postulate. It says that if two angles can form a linear pair, then they are supplementary. so <1+<2=180, 115+<2=180 becomes <2=65, so the answer is 65. This is how you can find the measure of the complement of <2.