Question

in the diagram below, m∠cih = 97° and m∠bgd = 43°. find m∠ihg. do not assume lines that appear straight are straight, but the figure is not otherwise drawn to scale.

Explanation:

Step1: Identify vertical - angles

$\angle BGD$ and $\angle AGC$ are vertical - angles. So, $m\angle AGC=m\angle BGD = 43^{\circ}$.

Step2: Use the angle - addition property

$\angle CH$ is an angle and $\angle AGC$ and $\angle HGC$ make up $\angle CH$. We know $m\angle CH = 97^{\circ}$ and $m\angle AGC=43^{\circ}$. Then $m\angle HGC=m\angle CH - m\angle AGC$.
$m\angle HGC=97^{\circ}-43^{\circ}=54^{\circ}$.

Step3: Find $\angle AHG$

$\angle AHG$ and $\angle HGC$ are vertical - angles. So, $m\angle AHG = m\angle HGC$.

Answer:

$54^{\circ}$