Question

structure find the measure of each angle in the diagram. (3y + 11)° 10y° (4x − 22)° (7x + 4)° (3y + 11)°: □° 10y°: □° (4x − 22)°: □° (7x + 4)°: □°

Explanation:

Step1: Solve for \( x \) using supplementary angles

\( (4x - 22) + (7x + 4) = 180 \) (linear pair, supplementary)
\( 11x - 18 = 180 \)
\( 11x = 198 \)
\( x = 18 \)

Step2: Solve for \( y \) using vertical angles

\( 3y + 11 = 4x - 22 \) (vertical angles are equal)
Substitute \( x = 18 \):
\( 3y + 11 = 4(18) - 22 \)
\( 3y + 11 = 72 - 22 \)
\( 3y + 11 = 50 \)
\( 3y = 39 \)
\( y = 13 \)

Step3: Calculate \( (3y + 11)^\circ \)

Substitute \( y = 13 \):
\( 3(13) + 11 = 39 + 11 = 50^\circ \)

Step4: Calculate \( 10y^\circ \)

Substitute \( y = 13 \):
\( 10(13) = 130^\circ \)

Step5: Calculate \( (4x - 22)^\circ \)

Substitute \( x = 18 \):
\( 4(18) - 22 = 72 - 22 = 50^\circ \)

Step6: Calculate \( (7x + 4)^\circ \)

Substitute \( x = 18 \):
\( 7(18) + 4 = 126 + 4 = 130^\circ \)

Answer:

\( (3y + 11)^\circ \): \( 50^\circ \)
\( 10y^\circ \): \( 130^\circ \)
\( (4x - 22)^\circ \): \( 50^\circ \)
\( (7x + 4)^\circ \): \( 130^\circ \)