Question

In the figure below, the measure of <4 is 130. What is the sum of the measure of <2 and <3

Answer 1

100 degrees.

Explanation:

<4 and <2 are adjacent angles so

m <4 + m<2 = 180

m<2 = 180 - 130 = 50 degrees.

m<3 = m<2 ( opposite angles).

Sum of <2 and < 3 = 2*50 = 100 degrees.

Answer 2

D 100°

Explanation:

Notice that angles 3 and 4 lie in the same line, which means they are supplementary angles, and supplementary angles always add up to 180°; therefore:

∠3 + ∠4 = 180°

∠3 + 130° = 180°

∠3 = 180° - 130°

∠3 = 50°

Notice that angles 2 and 3 are vertical angles. Since vertical angle are congruent (they have the say measure), ∠2 = ∠3 = 50°

Now we can add ∠2 and ∠3

∠2 + ∠3 = 50° + 50°

∠2 + ∠3 = 100°

We can conclude that the measure of ∠2 and ∠3 is 100°.