Question

⑤ a = b = c = d = e = f = h =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. So \(a = 110^{\circ}\) since it is vertical to the given \(110^{\circ}\) angle.

Step2: Use supplementary - angle property

The angle adjacent to \(a\) (let's call it \(b\)) is supplementary to \(a\). So \(b=180 - 110=70^{\circ}\).

Step3: Use vertical - angle property again

\(c=a = 110^{\circ}\) (vertical angles).

Step4: For the \(140^{\circ}\) angle

The angle adjacent to the \(140^{\circ}\) angle (let's call it \(e\)) is \(e = 180 - 140=40^{\circ}\). And \(d\) is vertical to the \(140^{\circ}\) angle, so \(d = 140^{\circ}\).

Step5: For the \(170^{\circ}\) angle

The angle adjacent to the \(170^{\circ}\) angle (let's call it \(h\)) is \(h=180 - 170 = 10^{\circ}\).

Step6: Find \(f\)

\(f\) and \(e\) are vertical angles, so \(f=e = 40^{\circ}\).

Answer:

\(a = 110^{\circ}\), \(b = 70^{\circ}\), \(c = 110^{\circ}\), \(d = 140^{\circ}\), \(e = 40^{\circ}\), \(f = 40^{\circ}\), \(h = 10^{\circ}\)