Question

question image
o. find the angle labeled with the question mark.

Explanation:

Step1: Find third angle of first triangle

The sum of angles in a triangle is \(180^\circ\). For the first triangle with angles \(30^\circ\) and \(80^\circ\), the third angle \(x\) is \(180 - 30 - 80 = 70^\circ\).

Step2: Find vertical opposite angle

The angle \(x = 70^\circ\) and the angle opposite to it (vertical angles) in the second triangle is also \(70^\circ\).

Step3: Find the unknown angle in second triangle

In the second triangle, with angles \(70^\circ\) (vertical opposite) and \(57^\circ\), the unknown angle \(y\) is \(180 - 70 - 57 = 53^\circ\).

Answer:

\(53^\circ\)