Question

question 5
not yet answered
marked out of 2.00
flag question
which statement about the angles in this diagram is false?
select one:
a. <c = 36°
b. <a = 36°
c. <d = 36°
d. <g = 36°

Explanation:

Step1: Identify supplementary - angle relationship

The angle of \(144^{\circ}\) and the angle adjacent to it (let's call it \(x\)) are supplementary. So \(x + 144^{\circ}=180^{\circ}\), then \(x = 180^{\circ}-144^{\circ}=36^{\circ}\).

Step2: Use properties of parallel - lines

Since the lines are parallel, corresponding angles are equal and alternate - interior angles are equal.
Angle \(a\) and the \(36^{\circ}\) angle we just found are corresponding angles, so \(\angle a = 36^{\circ}\).
Angle \(c\) and the \(36^{\circ}\) angle are alternate - interior angles, so \(\angle c = 36^{\circ}\).
Angle \(g\) and the \(36^{\circ}\) angle are corresponding angles, so \(\angle g = 36^{\circ}\).
Angle \(d\) and the \(144^{\circ}\) angle are corresponding angles, so \(\angle d=144^{\circ}
eq36^{\circ}\).

Answer:

C. \(\angle d = 36^{\circ}\)