Three angles have measures that add to  180°

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°

Two supplementary angles have the following measures:  m∠ABC=135° and m∠CBD=9x° . What is the equation to solve for x ?

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.

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

∠



?

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.

Two angles are supplementary and have measures  m∠QRS=(x+40)° and m∠SRT=x° . What is the measure of ∠QRS ?

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°