An obtuse angle is formed by two adjacent angles with measures (x−5)°

Question

and (3x)°
. If the resulting angle measure is 107°
, what is the angle measure of each of the two unknown angles? Round to the nearest whole number.(1 point)
Responses

32°
and 75°
32 degrees and 75 degrees

23°
and 84°
23 degrees and 84 degrees

20°
and 87°
20 degrees and 87 degrees

28°
and 79°

Answer 1

To find the measures of the two angles, we set up the equation based on the given information:

The two angles are:

• \( (x - 5)^\circ \)
• \( (3x)^\circ \)

These two angles add up to create an obtuse angle of \( 107^\circ \): \[ (x - 5) + (3x) = 107 \]

Combining like terms gives: \[ 4x - 5 = 107 \]

Next, we add \( 5 \) to both sides: \[ 4x = 112 \]

Now, divide by \( 4 \): \[ x = 28 \]

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

1. \( (x - 5) = (28 - 5) = 23^\circ \)
2. \( (3x) = (3 \times 28) = 84^\circ \)

Thus, the measures of the two angles are:

• \( 23^\circ \)
• \( 84^\circ \)

So, the correct response is \( 23^\circ \) and \( 84^\circ \).