Question

question 1: write down the sizes of the lettered angles. (a) (b) (c) (d) (e) (f)

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)
\(x = 150^{\circ}\) (corresponding angles), and \(y=180 - 150=30^{\circ}\) (supplementary angles).

(d)
\(x = 99^{\circ}\) (corresponding angles), \(y = 99^{\circ}\) (vertical - angles with \(x\)), \(z=180 - 99 = 81^{\circ}\) (supplementary to \(y\)).

(e)
\(x = 74^{\circ}\) (corresponding angles), \(y = 74^{\circ}\) (corresponding angles).

(f)
Let's first find \(x\). The angle adjacent to \(123^{\circ}\) 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) \(x = 150^{\circ}\), \(y = 30^{\circ}\)
(d) \(x = 99^{\circ}\), \(y = 99^{\circ}\), \(z = 81^{\circ}\)
(e) \(x = 74^{\circ}\), \(y = 74^{\circ}\)
(f) \(x = 57^{\circ}\), \(y = 70^{\circ}\)