Question

question 1: write down the sizes of the lettered angles. (a) 112° x (b) 75° x (c) y x 150° (d) 99° x y z (e) 74° x y (f) 123° y x 110°

Explanation:

Step1: Use corresponding - angles property

Corresponding angles formed by parallel lines and a transversal are equal.

Step2: Use supplementary - angles property

Supplementary angles add up to 180°.

(a)
Since the two lines are parallel, \(x = 112^{\circ}\) (corresponding angles).
(b)
Since the two lines are parallel, \(x=75^{\circ}\) (corresponding angles).
(c)
First, \(x = 180 - 150=30^{\circ}\) (supplementary angles). Then \(y = 150^{\circ}\) (corresponding angles to the \(150^{\circ}\) angle).
(d)
\(x = 99^{\circ}\) (vertically - opposite angles). \(y = 99^{\circ}\) (corresponding angles to \(x\)). \(z = 180 - 99 = 81^{\circ}\) (supplementary to \(y\)).
(e)
\(x = 74^{\circ}\) (corresponding angles). \(y = 74^{\circ}\) (corresponding angles to \(x\)).
(f)
Let's consider the parallel lines and transversals. First, find the angle adjacent to \(123^{\circ}\), which is \(180 - 123=57^{\circ}\). Then \(x = 57^{\circ}\) (corresponding angles). The angle adjacent to \(110^{\circ}\) is \(180 - 110 = 70^{\circ}\). Then \(y = 70^{\circ}\) (corresponding angles).

Answer:

(a) \(x = 112^{\circ}\)
(b) \(x = 75^{\circ}\)
(c) \(x = 30^{\circ},y = 150^{\circ}\)
(d) \(x = 99^{\circ},y = 99^{\circ},z = 81^{\circ}\)
(e) \(x = 74^{\circ},y = 74^{\circ}\)
(f) \(x = 57^{\circ},y = 70^{\circ}\)