Question

aa, bb, and ll intersect to form a triangle. which statement is true of ∠1 only if aa is perpendicular to bb? it is equal in measure to ∠4. it is complementary to ∠6.

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle4$ are vertical angles, so $\angle1=\angle4$ always, regardless of the perpendicularity of $AA'$ and $BB'$.

Step2: Recall linear - pair and supplementary - angle property

$\angle1$ and $\angle2$ form a linear - pair, so $\angle1+\angle2 = 180^{\circ}$. $\angle6$ and $\angle8$ form a linear - pair, so $\angle6+\angle8 = 180^{\circ}$. Also, $\angle2$ and $\angle8$ are vertical angles, so $\angle2=\angle8$. Then $\angle1$ and $\angle6$ are supplementary.

Answer:

It is equal in measure to $\angle4$.