Question

If the measure of angle 1 is (3 x minus 4) degrees and the measure of angle 2 is (4 x + 10) degrees, what is the measure of angle 2 in degrees?

A horizontal line. A line extends from the line to form a 90 degree angle. Another line cuts through the 2 lines to form angles 1 and 2, which total 90 degrees.
32 degrees
38 degrees
58 degrees
66 degrees

Answer 1

Given that angles 1 and 2 are supplementary and total 90 degrees, we can set up the equation:

\[
(3x - 4) + (4x + 10) = 90
\]

Now, let's simplify this equation:

\[
3x - 4 + 4x + 10 = 90
\]

Combine like terms:

\[
7x + 6 = 90
\]

Subtract 6 from both sides:

\[
7x = 84
\]

Now, divide by 7:

\[
x = 12
\]

Now that we have the value of \( x \), we can find the measure of angle 2:

\[
\text{Measure of angle 2} = 4x + 10 = 4(12) + 10
\]

Calculating that gives us:

\[
= 48 + 10 = 58
\]

Thus, the measure of angle 2 is \( \boxed{58} \) degrees.