Question

The measure of an angle is seventeen times the measure of its supplementary angle. What is the measure of each angle?

° ---- and °-----

Answer 1

[AI-generated answer — Bot GPT 3.5]

The sum of two supplementary angles is always 180 degrees. Let x be the measure of the smaller angle.

The larger angle is 17 times the measure of the smaller angle, so it is 17x.

Since these angles are supplementary, we have the equation:

x + 17x = 180

Combining like terms, we get:

18x = 180

Dividing both sides by 18, we find:

x = 10

So, the smaller angle is 10 degrees and the larger angle is 17 times that, which is 170 degrees.

Answer 2

An angle measures 44° less than the measure of its complementary angle. What is the measure of each angle?

Answer 3

[AI-generated answer — Bot GPT 3.5]

The sum of two complementary angles is always 90 degrees. Let x be the measure of the larger angle.

The smaller angle measures 44 degrees less than the complementary angle, so it is x - 44.

Since these angles are complementary, we have the equation:

x + (x - 44) = 90

Simplifying the equation, we get:

2x - 44 = 90
2x = 134
x = 67

So, the larger angle is 67 degrees and the smaller angle is 67 - 44 = 23 degrees.

Answer 4

so what is the answer

Answer 5

[AI-generated answer — Bot GPT 3.5]

The answer is:

- The larger angle measures 67 degrees
- The smaller angle, which is 44 degrees less than the larger angle, measures 23 degrees.

Answer 6

The measure of an angle is four times the measure of its complementary angle. What is the measure of each angle?

Answer 7

[AI-generated answer — Bot GPT 3.5]

Let x be the measure of the smaller angle. The complementary angle to x is 90 - x.

Given that the measure of an angle is four times the measure of its complementary angle, we have:

x = 4(90 - x)

Expanding and solving for x, we get:

x = 360 - 4x
5x = 360
x = 72

Therefore, the smaller angle measures 72 degrees, and the complementary angle (90 - 72) measures 18 degrees.

Answer 8

The measure of an angle is eleven times the measure of its supplementary angle. What is the measure of each angle?

Answer 9

[AI-generated answer — Bot GPT 3.5]

Let x be the measure of the smaller angle.

The larger angle is eleven times the measure of the smaller angle, so it is 11x.

Since these angles are supplementary, we have the equation:

x + 11x = 180

Combining like terms, we get:

12x = 180

Dividing both sides by 12, we find:

x = 15

So, the smaller angle is 15 degrees and the larger angle is 11 times that, which is 165 degrees.

Answer 10

An angle measures 82° more than the measure of its complementary angle. What is the measure of each angle?

Answer 11

[AI-generated answer — Bot GPT 3.5]

Let x be the measure of the smaller angle. The complementary angle to x is 90 - x.

Given that the angle measures 82° more than its complementary angle, we have:

x = (90 - x) + 82

Simplifying the equation, we get:

x = 90 - x + 82
x = 172 - x
2x = 172
x = 86

Therefore, the smaller angle measures 86 degrees, and the complementary angle (90 - 86) measures 4 degrees.