Three angles measures add to 180°

Question

and have the following measures: m∠ACB=(x+15)° , m∠BCD=(x+48)°, and m∠DCE=13°. What is the measure of ∠BCD?(1 point)
Responses

67°
67 degrees

100°
100 degrees

80°
80 degrees

52°

Answer 1

To find the measure of ∠BCD, we can use the fact that the sum of the angles in a triangle is 180°.

m∠ACB + m∠BCD + m∠DCE = 180°

Substituting the given measures, we have:

(x+15)° + (x+48)° + 13° = 180°

Combining like terms, we have:

2x + 76° = 180°

Subtracting 76° from both sides, we have:

2x = 104°

Dividing both sides by 2, we have:

x = 52°

Therefore, the measure of ∠BCD is (x+48)° = 52° + 48° = 100°.

So the correct answer is 100°.

Answer 2

Two angles are supplementary. They have the following measures: m∠QRS=(x+16)° and m∠SRT=(3x)° . What is the measure of ∠SRT ?(1 point)
m∠SRT=

Answer 3

To find the measure of ∠SRT, we use the fact that supplementary angles add up to 180°.

m∠QRS + m∠SRT = 180°

Substituting the given measures, we have:

(x+16)° + (3x)° = 180°

Combining like terms, we have:

4x + 16° = 180°

Subtracting 16° from both sides, we have:

4x = 164°

Dividing both sides by 4, we have:

x = 41°

Therefore, the measure of ∠SRT is (3x)° = 3(41°) = 123°.

So the measure of ∠SRT is 123°.

Answer 4

Two angles are supplementary. They have the following measures: m∠ACB=x° and m∠BCD=26° . What is the measure of ∠ACB ?(1 point)

Answer 5

To find the measure of ∠ACB, we use the fact that supplementary angles add up to 180°.

m∠ACB + m∠BCD = 180°

Substituting the given measures, we have:

x° + 26° = 180°

Combining like terms, we have:

x + 26 = 180

Subtracting 26 from both sides, we have:

x = 154

Therefore, the measure of ∠ACB is x° = 154°.

So the measure of ∠ACB is 154°.

Answer 6

Two supplementary angles have the following angle measures: m∠TUV=(2x−25)° and m∠VUW=110° . What is an equation to solve for x ? The equation should be in simplest terms.(1 point)
2x°+
°=
°

Answer 7

To solve for x, we use the fact that supplementary angles add up to 180°.

m∠TUV + m∠VUW = 180°

Substituting the given measures, we have:

(2x-25)° + 110° = 180°

Combining like terms, we have:

2x - 25 + 110 = 180

Simplifying the equation, we have:

2x + 85 = 180

Subtracting 85 from both sides, we have:

2x = 95

Dividing both sides by 2, we have:

x = 47.5

Therefore, the equation to solve for x in simplest terms is:

2x + 85 = 180

Answer 8

wo supplementary angles are ∠ABC=(3x+25)° and ∠CBD=32° . What is an equation to solve for x ? The equation should be in simplest terms.(1 point)
x°+
°=180°

Answer 9

To solve for x, we use the fact that supplementary angles add up to 180°.

∠ABC + ∠CBD = 180°

Substituting the given measures, we have:

(3x + 25)° + 32° = 180°

Combining like terms, we have:

3x + 57 = 180

Subtracting 57 from both sides, we have:

3x = 123

Dividing both sides by 3, we have:

x = 41

Therefore, the equation to solve for x in simplest terms is:

x + 57 = 180

Answer 10

Three angles have measures that add to 180°
. The angles have the following measures: m∠KLM=(x+30)° , m∠MLN=60° , and m∠NLP=(2x)° . What is an equation to solve for the unknown angle measures? Write the equation in simplest terms.(1 point)
x°+
°=180°

Answer 11

To solve for the unknown angle measures, we use the fact that the sum of the angles in a triangle is 180°.

m∠KLM + m∠MLN + m∠NLP = 180°

Substituting the given measures, we have:

(x+30)° + 60° + (2x)° = 180°

Combining like terms, we have:

3x + 90° = 180°

Subtracting 90° from both sides, we have:

3x = 90°

Dividing both sides by 3, we have:

x = 30°

Therefore, the equation to solve for the unknown angle measures in simplest terms is:

x + 90 = 180