Charles draws a supplementary angle and partitions it into 4 smaller angles totaling 180°. Angle X and Angle Y have the same measurement. Angle Z is 250% the value of Angles X and Y. Angle W is half the value of Angle X. Write an expression to determine the measurement of each angle.

Answer: w = 18°, x = 36°, y = 36°, z = 90°

Step-by-step explanation:

Let angle x be denoted as x

Since Angle X and Angle Y have the same measurement. This means: x = y

Angle Z is 250% the value of Angles X and Y. This means:

z = 250% * x = 2.5x

Angle W is half the value of Angle X. This means:

w = 1/2 * x = 0.5x

Add all the angles together and recall that:

w = 0.5x

x = x

y = x

z = 2.5x

W + X + Y + Z = 180

0.5x + x + x + 2.5x = 180

5x = 180

x = 180/5

x = 36°

w = 0.5x = 0.5 * 36° = 18°

x = x = 36°

y = x = 36°

z = 2.5x = 2.5 * 36° = 90°