Question

Two complementary angles have measures of (4x−5)° and (x+20)°. What is the value of x?
(4 Points)

15

17

19

25

Answer 1

Two angles are complementary if the sum of their measures is \(90^\circ\). Given the measures of the angles as \((4x - 5)^\circ\) and \((x + 20)^\circ\), we can set up the following equation:

\[
(4x - 5) + (x + 20) = 90
\]

Combining like terms, we get:

\[
4x - 5 + x + 20 = 90
\]
\[
5x + 15 = 90
\]

Next, we isolate \(x\) by first subtracting 15 from both sides:

\[
5x = 90 - 15
\]
\[
5x = 75
\]

Now, divide both sides by 5:

\[
x = \frac{75}{5}
\]
\[
x = 15
\]

Thus, the value of \(x\) is \(\boxed{15}\).