Question

15 find the measure of the \?\ or \x\. 51° ? 27° 93° ? = show hint

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Let the vertical - angle of the un - named angle in the second triangle be \(y\). Then \(y\) is equal to the un - named angle in the first triangle.

Step2: Apply the triangle - angle sum formula

The sum of angles in a triangle is \(180^{\circ}\).
For the second triangle: \(y + 27^{\circ}+93^{\circ}=180^{\circ}\).
\(y=180^{\circ}-(27^{\circ} + 93^{\circ})\).
\(y = 180^{\circ}-120^{\circ}=60^{\circ}\).
For the first triangle: Let the unknown angle be \(x\). Then \(x + 51^{\circ}+y = 180^{\circ}\).
Since \(y = 60^{\circ}\), we have \(x=180^{\circ}-(51^{\circ}+60^{\circ})\).
\(x = 180^{\circ}-111^{\circ}=69^{\circ}\).

Answer:

\(69^{\circ}\)