Solve Equations with Adjacent Angles Quick Check

Question

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

28°
and 79°
28 degrees and 79 degrees

23°
and 84°
23 degrees and 84 degrees

20°
and 87°
20 degrees and 87 degrees
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Answer 1

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

1. The two angles are (x - 5)° and (3x)°.
2. They form an obtuse angle measuring 107°.

Since they are adjacent angles, we can express this relationship as: \[ (x - 5) + (3x) = 107 \]

Now we combine like terms: \[ x - 5 + 3x = 107 \] \[ 4x - 5 = 107 \]

Next, we solve for \(x\): \[ 4x = 107 + 5 \] \[ 4x = 112 \] \[ x = 28 \]

Now we can find the measures of the two angles:

• The first angle: \( (x - 5) = (28 - 5) = 23° \)
• The second angle: \( (3x) = (3 \cdot 28) = 84° \)

So the measures of the two angles are 23° and 84°.

Therefore, the answer is: 23° and 84°.