Question

find the measure of each angle indicated.
1)

Explanation:

Step1: Find the angle in the lower triangle

The sum of angles in a triangle is \(180^{\circ}\).
Let the unknown angle in the lower triangle be \(x\).
\(x + 30^{\circ}+55^{\circ}=180^{\circ}\)
\(x=180^{\circ}-(30^{\circ} + 55^{\circ})\)
\(x = 95^{\circ}\)

Step2: Use the vertical - angle property

The angle \(x = 95^{\circ}\) and its vertical - opposite angle are equal.
Let the unknown angle in the upper triangle be \(y\).
In the upper triangle, using the angle - sum property of a triangle (\(180^{\circ}\)):
\(y+53^{\circ}+95^{\circ}=180^{\circ}\)
\(y=180^{\circ}-(53^{\circ}+95^{\circ})\)
\(y = 32^{\circ}\)

Answer:

\(32^{\circ}\)