Question

EC bisects <BED, m<ARV =11x- 12 and m<CED =4x +1. Find m<AEC
HELP!!​

Answer 1

Answer: AEC = 139

Explanation:

You first have to find x.

To find x, we need to add all the angles together to get 180°.

Since EC bisects BED, we know angle BEC and CED equal the same measure.

AEB + BEC + CED = 180°

(11x - 12) + (4x + 1) + (4x + 1) = 180°

Add like terms and solve

19x - 10 = 180

19x = 190

x = 10

Now, we substitute 'x' in AEB and BEC

AEB = 11x - 12

11 (10) - 12

AEB = 98

BEC = 4x + 1

4 (10) + 1

BEC = 41

98 + 41 = 139

AEC = 139

Answer 2

Answer:Angle AEC is 139 degrees.

Explanation:

Since line EC bisects angle BED, it divides angle BED equally into 2. This means that

Angle BEC = angle CED

If angle CED = 4x + 1

Therefore,

Angle BED = 2 × angle CED

= 2(4x + 1) = 8x + 2

The sum of the angles in a straight line is 180 degrees. Therefore

Angle AEB + angle BED = 180

Angle AEB = 11x - 12. Therefore

11x - 12 + 8x + 2 = 180

19x - 10 = 180

19x = 180 + 10 = 190

x = 190/19 = 10

Angle BEC = 4x + 1 = 4×10 + 1 = 41

Angle AEB = 11x - 12 = 11×10 - 12 = 98

Angle AEC = 41 + 98 = 139