Question

1. 8) e 85° 63° d f x m∠dex =

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In \(\triangle DEF\), let \(\angle E = 85^{\circ}\), \(\angle D=63^{\circ}\), and we want to find \(\angle DFE\). Let \(\angle DFE = x\). Then \(x + 85^{\circ}+63^{\circ}=180^{\circ}\).

Step2: Solve for \(\angle DFE\)

$$
LATEXBLOCK0
$$

Step3: Use linear - pair property

\(\angle DFX\) and \(\angle DFE\) form a linear - pair. A linear - pair of angles is supplementary, i.e., \(\angle DFX+\angle DFE = 180^{\circ}\). Let \(\angle DFX=y\), then \(y=180^{\circ}-\angle DFE\). Since \(\angle DFE = 32^{\circ}\), \(y = 180^{\circ}-32^{\circ}=148^{\circ}\).

Answer:

\(148^{\circ}\)