Question

Find the value of X. Then find the measure of each labeled angle.X=20;the labeled angles are 80 and 100 degrees X=20; both labeled angles are 90 degreesX=30; both labeled angles are 120 degreesX=30;both labeled angles are 150 degrees

Answer 1

Notice that the two given angles are generated by a transversal crossing a pair of parallel lines; therefore, those two angles are consecutive interior angles, and they are supplementary. Thus,

`\begin{gathered} 5x+4x=180\degree \\ \Rightarrow9x=180\degree \\ \Rightarrow x=20\degree \\ Therefore \\ \Rightarrow4x=80\degree \\ and \\ 5x=100\degree \end{gathered}`

Hence, the answer is x=20°, the labeled angles are 80°, and 100°, the first option.