Question

An obtuse angle is formed by two adjacent angles with measures (x + 10) °
and (3x) °
. If the resulting angle measure is 118 °
, what is the angle measure of each of the two unknown angles? (1 point)
Responses

43°
and 75°
43degree and 75degree

37°
and 81°
37degree and 81degree

20°
and 98°
20degree and 98degree

34°
and 84°

Answer 1

To find the measures of the two unknown angles, we need to set up the equation based on the information provided.

1. We know that the two adjacent angles are:
- First angle: \( (x + 10)^\circ \)
- Second angle: \( (3x)^\circ \)

2. The resulting angle formed by these two angles is given as \( 118^\circ \). Therefore, we can write the equation as:
\[
(x + 10) + (3x) = 118
\]

3. Simplifying the equation:
\[
x + 10 + 3x = 118
\]
\[
4x + 10 = 118
\]
\[
4x = 118 - 10
\]
\[
4x = 108
\]
\[
x = \frac{108}{4} = 27
\]

4. Now we can find the measures of the two angles:
- First angle: \( x + 10 = 27 + 10 = 37^\circ \)
- Second angle: \( 3x = 3 \cdot 27 = 81^\circ \)

Thus, the measures of the two adjacent angles are \( 37^\circ \) and \( 81^\circ \).

Therefore, the correct response is:
**37° and 81°**.