Question

1. ∠c and ∠d form a linear pair. the measure of ∠d is six more than twice the measure of ∠c. find m∠d.

Explanation:

Step1: Recall linear pair property

A linear pair of angles sums to \(180^\circ\). Let \(m\angle C = x\). Then \(m\angle D=2x + 6\) (since \(\angle D\) is six more than twice \(\angle C\)).

Step2: Set up equation

Since \(\angle C\) and \(\angle D\) are a linear pair, \(x+(2x + 6)=180\).
Simplify the left - hand side: \(3x+6 = 180\).
Subtract 6 from both sides: \(3x=180 - 6=174\).
Divide both sides by 3: \(x=\frac{174}{3}=58\).

Step3: Find \(m\angle D\)

Now that \(x = 58\) (which is \(m\angle C\)), substitute into the expression for \(m\angle D\): \(m\angle D=2(58)+6\).
First, calculate \(2\times58 = 116\), then \(116 + 6=122\).

Answer:

\(122^\circ\)