Q18 - Geometry

Question

State the measure of each angle.

• $\angle GOH$
  

Step-by-Step Solution

Answer

The measure of $\angle GOH$ is $\mathbf{20}\mathbf{°}$.

Step 1. Apply protractor postulate

On $\overline{AH}$ in a given plane, choose any point O between A and B.

Consider rays, $\overline{OA}$ and $\overline{OH}$ which are drawn from point O on $\overline{AH}$.

These rays results in pairing with the angles from 0 to 180 in such a way that:

The line $\overline{OA}$ is paired with 0, and $\overline{OH}$ with 180.

If $\overline{OG}$ is paired with x, and $\overline{OH}$ with y, then $m\angle GOH=\left|x-y\right|$.

Step 2. Observe the given figure and write the values of OG and OF

It can be observed from the figure that, $\overline{OG}$ is 160 and $\overline{OH}$ is 1800.

Step 3. Calculate m∠GOH.

$\begin{array}{l}m\angle GOH=\left|160-180\right|\\ =\left|-20\right|\\ =20°\end{array}$