Question

Look at the accompanying figure. Line AD || line EH. Line XY and line PQ are their transversals. If m∠CBF = 70° and m∠CGH = 55°. then



(1) m∠EFB = ......
(2) m∠GFY = ......
(3) m∠BCG = .....

Answer 1

It is given that line AD ║ line EH and lines XY and PQ are transversals.
Also,
m$\angle CBF$ = 70° and m$\angle CGH$ = 55°

(1) Consider the parallel lines AD and EH and the transversal XY.
$\angle CBF$ and $\angle EFB$ are alternate angles.
Because alternate angles are of the same measure, $\angle CBF$ = $\angle EFB$.
∴ $\angle EFB$ = 70° (∵ $\angle CBF$ = 70°)

(2) Consider the parallel lines AD and EH and the transversal XY.
$\angle CBF$ and $\angle GFY$ are corresponding angles.
Because corresponding angles are of the same measure, $\angle CBF$ = $\angle GFY$.
∴ $\angle GFY$ = 70° (∵ $\angle CBF$ = 70°)

(3) Consider the parallel lines AD and EH and the transversal PQ.
$\angle CGH$ and $\angle BCG$ are alternate angles.
Because alternate angles are of the same measure, $\angle CGH$ = $\angle BCG$.
∴ $\angle BCG$ = 55° (∵ $\angle CGH$ = 55°)