Question

if m∠dhe = 82°, then what is m∠dhf?

Explanation:

Step1: Recall linear - pair property

A linear pair of angles is supplementary, meaning the sum of the measures of two angles in a linear pair is 180°. ∠DHE and ∠DHF form a linear pair.
Let \(m\angle DHE = 82^{\circ}\) and \(m\angle DHF=x\). Then \(m\angle DHE + m\angle DHF=180^{\circ}\).

Step2: Solve for \(m\angle DHF\)

We have the equation \(82^{\circ}+x = 180^{\circ}\).
Subtract \(82^{\circ}\) from both sides: \(x=180^{\circ}- 82^{\circ}\).
\(x = 98^{\circ}\).

Answer:

\(98^{\circ}\)