Question

If EF bisects angle CEB, angle CEF=7x + 21 and angle FEB = 10x - 3, find the measure of DEB.

Answer 1

Answer: DEb = 26°

Step-by-step explanation:

Given information

CEF = 7x + 21

FEB = 10x - 3

Given expression deducted from the definition of the bisector

FEB = CEF

Substitute values into the expression

10x - 3 = 7x + 21

Subtract 7x on both sides

10x - 3 - 7x = 7x + 21 - 7x

3x - 3 = 21

Add 3 on both sides

3x - 3 + 3 = 21 + 3

3x = 24

Divide 3 on both sides

3x / 3 = 24 / 3

x = 8

Find the sum of the angle of CEF and FEB

 7x + 21 + 10x - 3

=7 (8) + 21 + 10 (8) - 3

=56 + 21 + 80 - 3

=77 + 80 - 3

=157 - 3

=154

Subtract 154 from the straight angle

DEB = 180 - 154

$\boxed{DEB = 26}$

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