Geometry: Common Core (15th Edition)

a) $\angle 4$ and the angle measuring $105^o$ are supplementary because of the same-side interior angles postulate, so $m\angle4=75$. Using the alternate interior angles theorem, we know $\angle4\cong\angle1$, so $m\angle1=75$. b) Using the vertical angles theorem, $\angle1\cong\angle2$, so $m\angle2=75$. c) The corresponding angles theorem tells us that $\angle5$ is congruent to the angle measuring $105^o$, so $m\angle5=105$ d) $\angle6$ forms an alternate interior pair with the angle that measures $105^o$. The alternate interior angles theorem tells us the pair is congruent. e) The vertical angles theorem tells us that $\angle7$ is congruent to the angle that measures $105^o$. f) $\angle8$ and $\angle1$ are supplementary because they form a linear pair. Since $m\angle1=75$, we know $m\angle8=105$.