Question

22find the measure of the \?\ or \x\.108°154°? =

Explanation:

Step1: Find the measure of ∠DEC

Use the linear - pair relationship.
$$\angle DEC=180^{\circ}-154^{\circ}=26^{\circ}$$

Step2: Use the triangle - angle sum theorem

In \(\triangle DCE\), the sum of interior angles is \(180^{\circ}\). Let the unknown angle be \(\angle D\).
$$\angle D + \angle C+\angle DEC=180^{\circ}$$
Substitute \(\angle C = 108^{\circ}\) and \(\angle DEC = 26^{\circ}\) into the formula.
$$\angle D=180^{\circ}-108^{\circ}-26^{\circ}$$
$$\angle D = 46^{\circ}$$

Answer:

\(46\)