Question

Solve for X ; X = _______
What is the measure of angle AED? ___
What is the measure of angle BEA? ___
What is the measure of angle DEC? ___
Angles AEB and AED sum to _ _ _ degrees so they are ______________ angles.
Angles DEC and AEB are ______________ angles so they must be E__________.

Answer 1

Step-by-step explanation:

6x+6=7x+3

on subtracting6both sides

6x=x+3

3x=x

x=2

Answer 2

Firstly, we'll find x

∠ DEC = ∠ AEB ( Opposite angle )

( 6x + 86 )° = ( 7x + 73 )°

6x + 86 = 7x + 73

7x - 6x = 86 - 73

x = 13

So

∠ DEC = ( 6x + 86 )° = ( (6 × 13) + 86 )° = 164°

similarly

∠ AEB = 164°

for ∠ AED

∠ AED = 180° - ∠ AEB ( linear pair )

∠ AED = 180° - 164

∠ AED = 16°

We can write ∠ AEB as ∠ BEA

∠ BEA = 164°

∠ AEB and ∠ AED sum to 180° degrees so they are Linear pair angles.

∠ DEC and ∠ AEB are opposite angles so they must be Equal