91Ó°ÊÓ

The position of all the angles is on a straight line which means that the sum of all the angles will be equal to 180°. By using this information make an equation.

$∠1+∠2+∠3+∠4=180°$

Angles having the same measurement are referred as the congruent angles.

Angles having the measurement of 90°when they added are referred as the complementary angles.

Make two equations by using the property of provided angles and the definitions.

$$\begin{gathered} ∠1=∠3 \\ ∠1+∠3=90° \end{gathered}$$

Using the properties of provided angles write the value of each angle.

$\begin{array}{c}2∠1=2∠2=90°\\ ∠1=∠3=45°\end{array}$

The relation between the lines $\stackrel{↔}{XY}$ and X is perpendicular which means that angles ∠1 and ∠2 represent the complementary angles. So make an equation by using this information after it uses the value of ∠1 and determines the value of ∠2.

$$\begin{gathered} ∠1+∠2=90° \\ 45+∠2=90° \\ ∠2=90°−45° \\ =45° \end{gathered}$$

The angles∠2 and∠3 are also representing the complementary angles so make an equation by using this information.

$∠2+∠3=90°$

The provided figure represents that the position of angles ∠2 and ∠3 is in the middle of $\stackrel{→}{XY}$and $\stackrel{→}{XZ}$. This represents that these two lines are having a relationship that is perpendicular so the provided relation between the lines can be concluded.