Question

1. using algebra ∠c and ∠d are supplementary. the measure of ∠d is eight times the measure of ∠c. find m∠c and m∠d.

Explanation:

Step1: Define variables and supplementary angle property

Let \( m\angle C = x \). Since \( \angle D \) is eight times \( \angle C \), \( m\angle D = 8x \). Supplementary angles add up to \( 180^\circ \), so \( x + 8x = 180^\circ \).

Step2: Solve for \( x \)

Combine like terms: \( 9x = 180^\circ \). Divide both sides by 9: \( x=\frac{180^\circ}{9}=20^\circ \).

Step3: Find \( m\angle D \)

Substitute \( x = 20^\circ \) into \( m\angle D = 8x \): \( m\angle D = 8\times20^\circ = 160^\circ \).

Answer:

\( m\angle C = 20^\circ \), \( m\angle D = 160^\circ \)