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

Answer 1

Since two angles are supplementary, their measures sum up to 180°.

Therefore, the equation representing this is:
(x+16)° + (3x)° = 180°

Now, let's solve for x:
(x+16)° + (3x)° = 180°
4x + 16° = 180°
4x = 180° - 16°
4x = 164°
x = 164°/4
x = 41°

Now, let's calculate the measure of ∠SRT:
m∠SRT = 3x = 3(41°) = 123°

Therefore, the measure of ∠SRT is 123°.

Answer 2

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 3

Since the two angles are supplementary, their measures sum up to 180°.

Therefore, the equation representing this is:
x° + 26° = 180°

Now, let's solve for x:
x° + 26° = 180°
x° = 180° - 26°
x° = 154°

Therefore, the measure of ∠ACB is 154°.

Answer 4

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)

Answer 5

Since two angles are supplementary, their measures sum up to 180°.

Therefore, the equation representing this is:
(2x-25)° + 110° = 180°

Now, let's solve for x:
2x-25° + 110° = 180°
2x+85° = 180°
2x = 180° - 85°
2x = 95°
x = 95°/2
x = 47.5°

Therefore, the equation to solve for x is 2x - 25 = 47.5.

Answer 6

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)

Answer 7

Since the three angles add up to 180°, the equation representing this is:
(x+30)° + 60° + (2x)° = 180°

Now, let's simplify the equation:
x + 30 + 60 + 2x = 180
3x + 90 = 180
3x = 180 - 90
3x = 90
x = 90/3
x = 30

Therefore, the equation to solve for the unknown angle measures is x + 30 + 60 + 2x = 180.