Question

n the diagram below,
←→
B
D
intersects
←→
C
E
. The measure of
∠
B
A
C
=
(
2
x
+
16
)
°
and the measure of
∠
C
A
D
=
(
x
−
10
)
°
.



2026_02_28_03_32_4927.png

What are the measures for each angle formed by
←→
B
D
and
←→
C
E
?



Drag and drop the correct angle measure for each angle into the table below. Answers may be used more than once.

Drag and drop an answer choice into each empty box below.
132º48º26º58º144º72º154º
∠
B
A
C

∠
C
A
D

∠
D
A
E

∠
B
A
E

Answer 1

Let x be such that (2x + 16) + (x − 10) = 180 (AB to AD is a straight line).
3x + 6 = 180 → x = 58.

Then
- ∠BAC = 2x + 16 = 2(58) + 16 = 132°
- ∠CAD = x − 10 = 58 − 10 = 48°

Vertical/opposite angles are equal, so
- ∠DAE = ∠BAC = 132°
- ∠BAE = ∠CAD = 48°

So the four angle measures are 132°, 48°, 132°, 48° respectively.