In the diagram,$\overrightarrow{UL}\perp \overleftarrow{MJ}$ and $m\angle JUK=x$. Express in terms of x the measures of the angles named.

a.$\angle LUK$

b.$\angle MUK$

Basically angles having the measurement of 90° are referred to as the right angles these angles are from the perpendicular relation between two lines.

The angles $\angle LUM$and $\angle LUJ$represents the right angles. The provided angle is a part of $\angle LUJ$so its value can be determined by subtracting the value of $\angle JUK$from $\angle LUJ$. By using this make an equation.

$\angle LUK=\angle LUM-\angle LUJ$

Substitute the value of $\angle LUM$and $\angle JUK$into the obtained equation.

$\angle LUK=90°-x°$

The provided angle is a part of straight-lineMUJ.

Every line that is straight having the measurement of 180°, therefore, the value of provided angle can be determined by subtracting the value of from $\angle JUK$the measurement of the straight line. By using this make an equation.

$\angle MUK=180°-\angle JUK$

Substitute the value of $\angle JUK$into the obtained equation.

$\angle MUK=180°-x°$