Question

angle addition postulate
find m∠fgk
46°

Explanation:

Step1: Recall angle - addition postulate

The sum of two adjacent angles with a common ray is equal to the larger angle formed by the non - common rays. Here, $\angle FGH$ and $\angle HGK$ are adjacent angles, and $\angle FGK=\angle FGH+\angle HGK$.

Step2: Identify known angles

We know that $\angle FGH = 46^{\circ}$ and $\angle HGK = 90^{\circ}$ (since the angle between the horizontal and vertical lines is a right - angle).

Step3: Calculate $\angle FGK$

$m\angle FGK=m\angle FGH + m\angle HGK=46^{\circ}+90^{\circ}=136^{\circ}$

Answer:

$136^{\circ}$