Question

question
find the missing angle.
answer attempt 5 out of 5

Explanation:

Step1: Find the base - angle of the isosceles triangle

Since the triangle is isosceles (marked with equal segments), and the non - right angle of the large right - triangle is \(40^{\circ}\), the base - angle of the isosceles triangle \(x\) can be found using the property of the exterior angle of a triangle. The base - angle of the isosceles triangle \(x=\frac{90 - 40}{2}=25^{\circ}\) (using the fact that the sum of angles in a right - triangle is \(180^{\circ}\) and the base - angles of an isosceles triangle are equal).

Step2: Use the exterior - angle property

The angle \(y\) (the missing angle) is an exterior angle of the isosceles triangle. By the exterior - angle property of a triangle (\(y=x + 40\)), substituting \(x = 25^{\circ}\), we get \(y=25+40 = 65^{\circ}\).

Step3: Use the linear - pair property

Since the missing angle \(z\) and \(y\) form a linear - pair (\(z + y=180^{\circ}\)), then \(z=180 - 65=115^{\circ}\)

Answer:

\(115^{\circ}\)