Question

It is given that $\angle XYZ=64°$ and $XY$ is produced to point $P$. Draw a figure from the given information. If ray $YQ$ bisects $\angle ZYP$, find $\angle XYQ$ and reflex $\angle QYP$.

Answer 1

Step 1: Find $\angle ZYP$

It is given, $XP$ is a straight line, so, $\angle XYZ+\angle ZYP=180°$

Substituting the value of $\angle XYZ=64°$, we get,

$64°+$ $\angle ZYP$ $=180°$

$\therefore$ $\angle ZYP=116°$

Step 2: Find $\angle XYQ$ and reflex $\angle QYP$

From the diagram, we know that

$\angle ZYP=\angle ZYQ+\angle QYP$

As $YQ$ bisects $\angle ZYP,\angle ZYQ$$=QYP$

Or, $\angle ZYP=2\angle ZYQ$

$\therefore \angle ZYQ=\angle QYP=58°$

Again, $\angle XYQ=\angle XYZ+\angle ZYQ$

Substituting the value of $\angle XYZ=64°$ and $ZYQ=\angle 58°$ , we get,

$\angle XYQ$ $=64°+58°=122°$

Now, reflex $\angle QYP=180°+$ $\angle XYQ$

The value of $\angle XYQ$ $=122°$.

So, reflex $\angle QYP=180°+122°=302°$

Hence, $\angle XYQ$ $=122°$ and reflex $\angle QYP=302°$.