∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left parenthesis, x, plus, 27, right parenthesis, degrees∠1=(x+27)

Question

∘
and mangle, 2, equals, left parenthesis, 2, x, plus, 20, right parenthesis, degrees∠2=(2x+20)
∘
, then find the value of x.

Answer 1

Since angles 1 and 2 are vertical angles, they are equal to each other. We can set up the equation:

\[ x + 27 = 2x + 20 \]

Now, we'll solve for \(x\):

1. Subtract \(x\) from both sides:

\[ 27 = x + 20 \]

2. Subtract 20 from both sides:

\[ 27 - 20 = x \]

3. Simplify:

\[ 7 = x \]

Thus, the value of \(x\) is

\[ \boxed{7} \]