Question

find the measures of the angles marked x and y. remember that (1) the sum of the measures of the angles of a triangle is 180° and (2) supplementary angles have a sum of 180°. x = \boxed{} and y = \boxed{} (simplify your answer. do not include the degree symbol in your answer.)

Explanation:

Step1: Identify supplementary angles

The angle \( y \) and \( (2x + 50) \) are supplementary, so \( y + (2x + 50) = 180 \), which gives \( y = 180 - 2x - 50 = 130 - 2x \). Also, the triangle is right - angled, so the sum of angles in the triangle is \( 90 + x + y = 180 \).

Step2: Substitute y into triangle angle sum

Substitute \( y = 130 - 2x \) into \( 90 + x + y = 180 \). We get \( 90 + x+(130 - 2x)=180 \). Simplify the left - hand side: \( 90 + 130+x - 2x=180 \), \( 220 - x = 180 \).

Step3: Solve for x

Subtract 220 from both sides: \( -x=180 - 220=-40 \). Multiply both sides by - 1: \( x = 40 \).

Step4: Solve for y

Substitute \( x = 40 \) into \( y = 130 - 2x \). Then \( y=130-2\times40=130 - 80 = 50 \).

Answer:

\( x = 40 \) and \( y = 50 \)