∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left bracket, 5, x, plus, 5, right bracket, degrees∠1=(5x+5)

Question

∘
and mangle, 2, equals, left bracket, 6, x, minus, 8, right bracket, degrees∠2=(6x−8)
∘
, then find the value of x.

Answer 1

Since ∠1 and ∠2 are vertical angles, they are equal to each other.

So, we have:

5x + 5 = 6x - 8

Subtracting 5x from both sides:

5 = x - 8

Adding 8 to both sides:

13 = x

Therefore, the value of x is 13.

Answer 2

∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left bracket, 6, x, plus, 21, right bracket, degrees∠1=(6x+21)
∘
and mangle, 2, equals, left bracket, 5, x, plus, 25, right bracket, degrees∠2=(5x+25)
∘
, then find the value of x

Answer 3

Since ∠1 and ∠2 are vertical angles, they are equal to each other.

So, we have:

6x + 21 = 5x + 25

Subtracting 5x from both sides:

x + 21 = 25

Subtracting 21 from both sides:

x = 4

Therefore, the value of x is 4.