Question

in the diagram below, m∠cih = 100° and m∠bgd = 43°. find m∠ahf.
step angle reason
1 m∠cih = 100° given
2 m∠bgd = 43° given
try m∠□ = □° select a reason

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. $\angle BGD$ and $\angle AGF$ are vertical angles.
Since $m\angle BGD = 43^{\circ}$, then $m\angle AGF=43^{\circ}$ (Vertical - angles are congruent).

Step2: Identify linear - pair

$\angle CIH$ and $\angle HIG$ form a linear - pair. A linear - pair of angles is supplementary, so $m\angle CIH+m\angle HIG = 180^{\circ}$.
Given $m\angle CIH = 100^{\circ}$, then $m\angle HIG=180 - 100=80^{\circ}$.

Step3: Find $m\angle AHF$

$\angle AHF$ and $\angle HIG$ are vertical angles. Since vertical angles are equal, $m\angle AHF=m\angle HIG$.
So $m\angle AHF = 80^{\circ}$.

Answer:

$m\angle AHF = 80^{\circ}$