Question

n the pair of supplementary angles shown below, the measure of the smaller angle is 36°.



Complete the equation that could be used to represent this situation. Then, solve the equation to complete the sentences.

180
36
56
144
38
34
90
120



(4x - 8) + (blank) = (blank)
The value of x is (blank(
The measure of the larger angle is (blank)

Answer 1

To find the supplementary angle that corresponds to the smaller angle of 36°, we know that the sum of supplementary angles is 180°.

Let’s denote the larger angle as \( L \). Since the smaller angle is given as 36°, we can set up the equation:

\[
L + 36° = 180°
\]

To find \( L \), rearranging gives us:

\[
L = 180° - 36° = 144°
\]

Now we need to express this using the equation in the format \( (4x - 8) + (blank) = (blank) \).

If we set \( 4x - 8 \) to be the larger angle \( L \), then:

\[
4x - 8 + 36 = 180
\]

Now substituting into the blanks:

1. The equation is \( (4x - 8) + 36 = 180 \).
2. To solve for \( x \):
\[
4x - 8 + 36 = 180
\]
\[
4x + 28 = 180
\]
\[
4x = 180 - 28
\]
\[
4x = 152
\]
\[
x = \frac{152}{4} = 38
\]

3. The value of \( x \) is 38.
4. The measure of the larger angle (which we already calculated) is 144°.

So, the completed sentences are:

- The equation is \( (4x - 8) + 36 = 180 \).
- The value of \( x \) is 38.
- The measure of the larger angle is 144°.