Question

C. When two lines intersect, the

angles that lie on opposite sides of
the intersection point are called
vertical angles. For example, in
the diagram at the right, AED and
CEB are vertical angles. Name
another pair of vertical angles.
A
230
.19
E
DEB and AEC
9
B
d. Using the diagram at the right,
determine the measure of AEC,
DEB, and CEB if x = 23°. Show
all your work.

Answer 1

AEC=BED=157°

Explanation:

AEC + CEB + BED + x = 360°

since CEB and x are vertical angles, they are equal.

Also, AEC = BED (same reason)

therefore,

2AEC+ 23° + 23° = 360°

2AEC + 46° = 360°

2AEC = 360° - 46°

2AEC = 314°

AEC = 157°

BED also = 157°