Question

A figure displays two adjacent complementary angles with measures (x+3)°
and (4x−2)°
. What is the equation of the angles measures? one answer is the number

Answer 1

Complementary angles are two angles whose measures add up to \(90^\circ\). Given the two angles are \( (x+3)^\circ \) and \( (4x-2)^\circ \), you can set up the following equation:

\[
(x + 3) + (4x - 2) = 90
\]

Now, simplify and solve for \(x\):

\[
x + 3 + 4x - 2 = 90
\]
\[
5x + 1 = 90
\]
\[
5x = 90 - 1
\]
\[
5x = 89
\]
\[
x = \frac{89}{5}
\]
\[
x = 17.8
\]

Now substitute \(x\) back into the expressions for the angles:

1. For the first angle:
\[
x + 3 = 17.8 + 3 = 20.8^\circ
\]

2. For the second angle:
\[
4x - 2 = 4(17.8) - 2 = 71.2 - 2 = 69.2^\circ
\]

To summarize, the equation of the angles measures is:
\[
(x + 3) + (4x - 2) = 90
\]
with \( x = 17.8 \), resulting in angles of \( 20.8^\circ \) and \( 69.2^\circ \).