Question

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.$\angle MUK$

Short answer

a. The value for a given angle is $90°-x°$.

b. The value for a given angle is $180°-x°$.

Step-by-step solution

Part a. Step 1. Definition of the right angle.

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

Part a. Step 2. Determine the angles that are right angles and make an equation.

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.

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

Part a. Step 3. Determine the value of the given angle.

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

$\angle LUK=90°-x°$

Part b. Step 1. Observe the provided figure.

The provided angle is a part of straight-lineMUJ.

Part b. Step 2. Make an equation.

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.

$\angle MUK=180°-\angle JUK$

Part a. Step 3. Determine the value of the given angle.

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

$\angle MUK=180°-x°$