Question

1. determine the value of each angle.

a)

Explanation:

Step1: Find \( f \)

Vertical - angles are equal. So \( f = 110^{\circ} \).

Step2: Find \( p \)

\( f + p=180^{\circ} \) (supplementary angles). Then \( p = 180^{\circ}-f \). Substitute \( f = 110^{\circ} \), so \( p=70^{\circ} \).

Step3: Find \( h \)

The triangle is isosceles (two sides are equal, marked as \( h \)). The base - angles of an isosceles triangle are equal. Let the base - angles be \( h \). Using the angle - sum property of a triangle (\( 180^{\circ} \)), \( h + h+p = 180^{\circ} \). Substitute \( p = 70^{\circ} \), we get \( 2h+70^{\circ}=180^{\circ} \). Then \( 2h=180^{\circ}-70^{\circ}=110^{\circ} \), so \( h = 55^{\circ} \).

Step4: Find \( u \)

\( u = h \) (alternate - interior angles for parallel lines). So \( u = 55^{\circ} \).

Answer:

\( f = 110^{\circ}\), \(p = 70^{\circ}\), \(h = 55^{\circ}\), \(u = 55^{\circ}\)