Question

find the measure of \\( \angle hpr \\).

Explanation:

Step1: Use the property of linear pair

Angles \(7y + 106\) and \(6y+109\) form a linear pair. So, \((7y + 106)+(6y + 109)=180\).

Step2: Solve the equation for \(y\)

Combine like - terms: \(7y+6y+106 + 109=180\), \(13y+215 = 180\).
Subtract \(215\) from both sides: \(13y=180 - 215=-35\), \(y = - 5\).

Step3: Find the measure of \(\angle HPR\)

Substitute \(y=-5\) into \(6y + 109\).
\(6\times(-5)+109=-30 + 109 = 79\).

Answer:

\(79^{\circ}\)