Asked by Enter Name Here

Three angles have measures that add to  180°
180
°
. They have the following angle measures:  m∠ABC=(x−6)° , m∠CBD=(4x−14)° , and m∠DBE=5x° . What is the equation to solve for x ?
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Two supplementary angles have the following measures:  m∠ABC=135° and m∠CBD=9x° . What is the equation to solve for x ?
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Use facts about supplementary angles to solve the following problem. Two angles are supplementary and have measures  m∠ABC=15° and m∠CBD=x° . What is the value of m∠CBD

∠



?
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Two angles are supplementary and have measures  m∠QRS=(x+40)° and m∠SRT=x° . What is the measure of ∠QRS ?
Answered by GPT 3.5
To find the equation to solve for x, we need to use the fact that the sum of the angle measures is equal to 180°.

We can set up the equation as follows:

(m∠ABC) + (m∠CBD) + (m∠DBE) = 180°

Substituting the given angle measures, we have:

(x - 6) + (4x - 14) + (5x) = 180°

Now we can solve for x by combining like terms:

10x - 20 = 180°

Adding 20 to both sides:

10x = 200°

Finally, we divide both sides by 10 to solve for x:

x = 20°
Answered by GPT 3.5
To find the equation to solve for x, we know that two angles are supplementary if their measures add up to 180 degrees.

We can set up the equation as follows:

m∠ABC + m∠CBD = 180°

Substituting the given angle measures, we have:

135° + 9x° = 180°

Now we can solve for x by isolating the variable on one side of the equation:

9x° = 180° - 135°

9x° = 45°

Dividing both sides of the equation by 9:

x° = 45°/9

x° = 5°

Therefore, the equation to solve for x is 9x = 45.
Answered by GPT 3.5
Since the two angles are supplementary, their measures add up to 180 degrees.

We can set up the equation as follows:

m∠ABC + m∠CBD = 180°

Substituting the given angle measures, we have:

15° + x° = 180°

Now we can solve for x by isolating the variable on one side of the equation:

x° = 180° - 15°

x° = 165°

Therefore, the value of ∠CBD is 165 degrees.
Answered by GPT 3.5
Since the two angles are supplementary, their measures add up to 180 degrees.

We can set up the equation as follows:

m∠QRS + m∠SRT = 180°

Substituting the given angle measures, we have:

(x + 40)° + x° = 180°

Now we can solve for x by combining like terms:

2x + 40° = 180°

Subtracting 40° from both sides:

2x = 140°

Finally, we divide both sides by 2 to solve for x:

x = 70°

Therefore, the measure of ∠QRS is:

m∠QRS = x + 40° = 70° + 40° = 110°