Question

27 find the measure of the \?\ or \x\.
? =

Explanation:

Step1: Find the vertical angle

Vertical angles are equal. Let the vertical angle be \(y\).
In the first triangle, using the angle - sum property of a triangle (\(180^{\circ}\) in a triangle), \(y=180^{\circ}-(35^{\circ}+50^{\circ})\).

$$y = 180^{\circ}-85^{\circ}=95^{\circ}$$

Step2: Calculate the unknown angle

In the second triangle, again using the angle - sum property of a triangle. Let the unknown angle be \(x\).
\(x = 180^{\circ}-(y + 52^{\circ})\)
Substitute \(y = 95^{\circ}\) into the equation:

$$x=180^{\circ}-(95^{\circ}+52^{\circ})=180^{\circ}-147^{\circ}=33^{\circ}$$

Answer:

\(33\)