Question

find the unknown angle measures.
figure is not to scale
x =
y =
question help: video 1 video 2

Explanation:

Step1: Find \(x\)

The sum of angles in a triangle is \(180^{\circ}\).
For the large triangle: \(x + 49^{\circ}+51^{\circ}+71^{\circ}=180^{\circ}\)
\(x+171^{\circ}=180^{\circ}\)
\(x = 180^{\circ}-171^{\circ}\)
\(x = 9^{\circ}\)

Step2: Find \(y\)

For the triangle with angles \(49^{\circ},x^{\circ},y^{\circ}\)
\(y=180^{\circ}-(49^{\circ}+x^{\circ})\)
Substitute \(x = 9^{\circ}\)
\(y=180^{\circ}-(49^{\circ}+9^{\circ})\)
\(y=180^{\circ}-58^{\circ}\)
\(y = 122^{\circ}\)

Answer:

\(x = 9\), \(y = 122\)