Question

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

Explanation:

Step1: Use corresponding - angle property

For parallel - lines cut by a transversal, corresponding angles are equal.

Step2: Use supplementary - angle property

Supplementary angles add up to 180°.

(a)
Since the two lines are parallel and the given angle of 112° and angle \(x\) are corresponding angles, \(x = 112^{\circ}\).

(b)
The angle of 75° and angle \(x\) are corresponding angles, so \(x=75^{\circ}\).

(c)
The angle of 150° and angle \(x\) are corresponding angles, so \(x = 150^{\circ}\). The angle \(y\) and the 150° angle are supplementary. So \(y=180 - 150=30^{\circ}\).

(d)
The angle of 97° and angle \(x\) are corresponding angles, so \(x = 97^{\circ}\). Angle \(y\) and angle \(x\) are supplementary, so \(y=180 - 97 = 83^{\circ}\). Angle \(z\) and angle \(x\) are corresponding angles, so \(z = 97^{\circ}\).

(e)
The angle of 74° and angle \(x\) are corresponding angles, so \(x = 74^{\circ}\). The angle \(y\) and the 74° angle are supplementary, so \(y=180 - 74=106^{\circ}\).

(f)
Let's first find the angle adjacent to 123°. It is \(180 - 123=57^{\circ}\). This 57° angle and angle \(x\) are corresponding angles, so \(x = 57^{\circ}\).
The angle of 110° and angle \(y\) are corresponding angles, so \(y = 110^{\circ}\).

Answer:

(a) \(x = 112^{\circ}\)
(b) \(x=75^{\circ}\)
(c) \(x = 150^{\circ},y = 30^{\circ}\)
(d) \(x = 97^{\circ},y = 83^{\circ},z = 97^{\circ}\)
(e) \(x = 74^{\circ},y = 106^{\circ}\)
(f) \(x = 57^{\circ},y = 110^{\circ}\)