Q22 - Geometry

Question

State the measure of each angle.

• $\angle HOA$
  

Step-by-Step Solution

Answer

The measure of $\angle HOA$ is $\mathbf{180}\mathbf{°}$.

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

Step 2. Observe the given figure and write the values of OA and OH.

It can be observed from the figure that, $\overline{OA}$ is 0 and $\overline{OH}$ is 180.

Step 3. Calculate m∠HOA

$\begin{array}{l}m\angle HOA=\left|0-180\right|\\ =\left|180\right|\\ =180°\end{array}$