Question

Two adjacent angles, ∠1

and ∠2
, form a resulting angle with measure 135°. If m∠1=(2x)° and m∠2=(2x+7)°, what are the two unknown angle measures?(1 point)
m∠1=
°, m∠2=
°

Answer 1

[AI-generated answer — Bot GPT 3.5]

Given that m∠1 = (2x)° and m∠2 = (2x+7)°, we know that the sum of the two angles is equal to 135°.

So, (2x)° + (2x+7)° = 135°

Combining like terms, we have 4x + 7 = 135.

Subtracting 7 from both sides, we get 4x = 128.

Dividing both sides by 4, we have x = 32.

Therefore, m∠1 = (2(32))° = 64°, and m∠2 = (2(32)+7)° = 71°.

So, the two unknown angle measures are m∠1 = 64° and m∠2 = 71°.

Answer 2

Angle Pairs Unit Test

5 of 155 of 15 Items

Question
A figure displays two complementary nonadjacent angles. If one of the angles has a measure of 39° , what is the other angle measure?(1 point)
°

Answer 3

[AI-generated answer — Bot GPT 3.5]

Complementary angles are two angles whose measures add up to 90°.

Given that one of the angles has a measure of 39°, we can subtract this measure from 90° to find the measure of the other angle.

90° - 39° = 51°

Therefore, the measure of the other angle is 51°.

Answer 4

A figure shows two nonadjacent angles with measures (2x+3)° and 2x° . If the angles are complementary, what is the equation for the angle measures?(1 point)

(
)° + 2x° =
°

Answer 5

[AI-generated answer — Bot GPT 3.5]

Given that the angles are complementary, the sum of their measures is 90°.

So, (2x+3)° + 2x° = 90°.

Combining like terms, we have 4x + 3 = 90.

Subtracting 3 from both sides, we get 4x = 87.

Dividing both sides by 4, we have x = 21.75.

Therefore, the equation for the angle measures is (2(21.75) + 3)° + 2(21.75)° = 90°.

Simplifying, we have (43.5 + 3)° + 43.5° = 90°.

Which gives us 46.5° + 43.5° = 90°.

So, the equation for the angle measures is 46.5° + 43.5° = 90°.

Answer 6

Two complementary angles have measures (2x)° and (3x)° . What is the value of x and the two angle measures?(2 points)

x=
, (2x)°=
°, and (3x)°=
°

Answer 7

[AI-generated answer — Bot GPT 3.5]

Complementary angles have measures that add up to 90°.

Given that the measures of the angles are (2x)° and (3x)°, we can set up the equation:

(2x)° + (3x)° = 90°

Combining like terms, we have 5x = 90.

Dividing both sides by 5, we get x = 18.

Therefore, x = 18, and substituting x into the angle measures, we have:

(2(18))° = 36°, and (3(18))° = 54°.

So, x = 18, (2x)° = 36°, and (3x)° = 54°.

Answer 8

Angles j and k are supplementary angles. What is m∠j if m∠k=117° ?(1 point)

°

Answer 9

[AI-generated answer — Bot GPT 3.5]

Supplementary angles are two angles whose measures add up to 180°.

Given that m∠k = 117°, we can subtract this measure from 180° to find the measure of m∠j.

180° - 117° = 63°

Therefore, m∠j = 63°.

Answer 10

Two supplementary angles have measures m∠ABC=105° and m∠CBD=(3x−24)° . What is the equation to solve for x ? (1 point)

(3x−24)°+
°=
°

Answer 11

[AI-generated answer — Bot GPT 3.5]

Supplementary angles have measures that add up to 180°.

Given that m∠ABC = 105° and m∠CBD = (3x - 24)°, we can set up the equation:

105° + (3x - 24)° = 180°

Combining like terms, we have 3x - 24 + 105 = 180°

Simplifying further, we get 3x + 81 = 180°

Subtracting 81 from both sides, we have 3x = 99°

Dividing both sides by 3, we get x = 33°

Therefore, the equation to solve for x is (3x - 24)° + 105° = 180°, which simplifies to 3x - 24 + 105 = 180°.