Question

find the value of the variable and the measure of each labeled angle.
$(x + 10)^circ$
$(3x - 34)^circ$
x = 22
(type a whole number.)
$(x + 10)^circ = 32 ^circ$
(type a whole number.)
$(3x - 34)^circ = \square^circ$
(type a whole number.)

Explanation:

Step1: Identify the relationship (vertical angles)

The two angles \((x + 10)^\circ\) and \((3x - 34)^\circ\) are vertical angles, so they are equal. We already know \(x = 22\), so we substitute \(x\) into \((3x - 34)^\circ\).

Step2: Substitute \(x = 22\) into the expression

Substitute \(x = 22\) into \(3x - 34\):
\(3\times22 - 34\)
First, calculate \(3\times22 = 66\), then \(66 - 34 = 32\).

Answer:

\(32\)