Question

∠c and ∠d are vertical angles with (mangle c=-x + 26) and (mangle d = 2x-10). what is (mangle d)? enter your answer in the box.

Explanation:

Step1: Use vertical - angle property

Since vertical angles are equal, we set \(m\angle C=m\angle D\). So, \(-x + 26=2x-10\).

Step2: Solve for \(x\)

Add \(x\) to both sides: \(26 = 3x-10\). Then add 10 to both sides: \(36 = 3x\). Divide both sides by 3, we get \(x = 12\).

Step3: Find \(m\angle D\)

Substitute \(x = 12\) into the expression for \(m\angle D\), \(m\angle D=2x - 10=2\times12-10\). Calculate \(2\times12-10=24 - 10=14\).

Answer:

14