Question
An obtuse angle is formed by two adjacent angles with measures (x - 5)* and (3x)*. Iif the resulting angle measure is 107*, what is the angle measure of each of the two unknown angles? (1 point)
• 28* and 79*
• 23* and 84*
• 32* and 75*
• 20* and 87*
• 28* and 79*
• 23* and 84*
• 32* and 75*
• 20* and 87*
Answers
GPT 3.5
Let's solve for x first.
If the obtuse angle is formed by two angles, then the sum of those two angles should be greater than 90° (since an obtuse angle is greater than 90°).
(x - 5)* + (3x)* > 90°
4x - 5 + 3x > 90
7x - 5 > 90
7x > 95
x > 13.57
Now, let's substitute x back into the given angles to find the measures of each unknown angle.
First angle: (x - 5)*
= (13.57 - 5)*
= 8.57°
Second angle: (3x)*
= (3 * 13.57)*
= 40.71°
The angle measures of the two unknown angles are approximately 8.57° and 40.71°.
The answer is not listed among the given choices.
If the obtuse angle is formed by two angles, then the sum of those two angles should be greater than 90° (since an obtuse angle is greater than 90°).
(x - 5)* + (3x)* > 90°
4x - 5 + 3x > 90
7x - 5 > 90
7x > 95
x > 13.57
Now, let's substitute x back into the given angles to find the measures of each unknown angle.
First angle: (x - 5)*
= (13.57 - 5)*
= 8.57°
Second angle: (3x)*
= (3 * 13.57)*
= 40.71°
The angle measures of the two unknown angles are approximately 8.57° and 40.71°.
The answer is not listed among the given choices.