Question

in the diagram (mangle1 = 42^{circ}) and (mangle4 = 99^{circ}). find (mangle3) find (mangle dge) find (mangle cge) find (mangle2) find (mangle agc)

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of angles around a point is $360^{\circ}$, and in the intersection of lines, vertical - angles are equal. Also, the sum of angles in a linear pair is $180^{\circ}$. We know that $\angle1$ and $\angle2$ are vertical angles, $\angle3$ and $\angle4$ are vertical angles.

Step2: Use vertical - angle property

Since vertical angles are equal, $\angle3=\angle4$. Given $m\angle4 = 99^{\circ}$, so $m\angle3=99^{\circ}$.

Answer:

$99^{\circ}$