Chapter 7.3, Problem 4PSA

Solution

To Calculate: The measure of the $\angle 1$

The required measure of $\angle 1$ is ${80}^{\circ }$

Given information: $m\angle F=110$ , $m\angle G=80$ and $m\angle H=74$ is provided in the question which will help to find the solution.

Formula used: Here, we are using the formula

$(n-2)\times 180$

Calculation: $m\angle F+m\angle G+m\angle H+m\angle E={360}^{\circ }$

➔ $110+80+74+\angle E={360}^{\circ }$

➔ $\angle E={96}^{\circ }$

And, $\angle 1+\angle E={180}^{\circ }$ (linear angle)

➔ $\angle 1+{96}^{\circ }={180}^{\circ }$

➔ $\angle 1={80}^{\circ }$

Hence, the required measure $\angle 1$ is ${80}^{\circ }$