Question

∠E and ∠F are vertical angles with m∠E=5x+10 and m∠F=7x−12 . What is the value of x?

Answer 1

Answer:  11

Step-by-step explanation:

We are given that ∠E and ∠F are vertical angles with m∠E=5x+10 and m∠F=7x−12 .

We know that vertical angles are congruent, then their measures must be equal.

i.e. if ∠E and ∠F are vertical angles.

⇒ m∠E=m∠F

$\Rightarrow\ 5x+10=7x-12$   [Substitute the measures of ∠E and ∠F]

Subtract 5x from both sides , we get

$10=2x-12$

Add 12 on both sides , we get

$22=2x$

Divide both sides by 2 , we get

$11=x$ or x=11

Hence, the value of x= 11

Answer 2

Vertical angles are equal

5x + 10 = 7x - 12
5x - 7x = -12 - 10
-2x = -22
x = -22/-2
x = 11 <===