Question

∠1 and angle, 2∠2 are vertical angles. If mangle, 1, equals, left parenthesis, 5, x, plus, 1, right parenthesis, degrees∠1=(5x+1)
∘
and mangle, 2, equals, left parenthesis, 4, x, plus, 3, right parenthesis, degrees∠2=(4x+3)
∘
, then find the value of x.

Answer 1

Since angles 1 and 2 are vertical angles, they are equal. So we can set their measures equal to each other:

\[
5x + 1 = 4x + 3
\]

To solve for \(x\), first, subtract \(4x\) from both sides:

\[
5x - 4x + 1 = 3
\]

This simplifies to:

\[
x + 1 = 3
\]

Next, subtract 1 from both sides:

\[
x = 3 - 1
\]

Thus,

\[
x = 2
\]

So the value of \(x\) is \(2\).