There are two complementary angles, ∠5 and ∠6 . If m∠5=39° , what equation can you write to solve for m∠6 ?

m∠6 + 39° = 180°

Two angles, ∠1 and ∠2 , in a diagram are supplementary. If m∠1=77° , what equation can you write to solve for m∠2 ? Let m∠2=x°

responses:
x° = 90° - 77°
x° = 77°
x° + 77° = 180°
x° + 77° = 90°

x° + 77° = 180°

There are angles whose measures add to 180° . Their measures are: m∠A=67° , m∠B=(2x+20)° , and m∠C=x° . What is the measure of ∠B ?

62°
31°
180°
82°

To find the measure of ∠B, we can set up an equation:

m∠A + m∠B + m∠C = 180°

Given that m∠A = 67°, m∠B = (2x + 20)°, and m∠C = x°, we can substitute these values into the equation:

67° + (2x + 20)° + x° = 180°

Combine like terms:

3x + 87° = 180°

Subtract 87° from both sides:

3x = 93°

Divide both sides by 3:

x = 31°

Now we can substitute x = 31° into m∠B = (2x + 20)°:

m∠B = 2(31°) + 20° = 82°

Therefore, the measure of ∠B is 82°.

If there are two supplementary angles, ∠D and ∠E , where m∠D=(4x+8)° and m∠E=(x+17)° , and ∠F is a vertical angle with ∠D , what is the measure of ∠F ?

48°
31°
124°
132°

To find the measure of ∠F, we need to use the properties of vertical angles. Vertical angles are opposite angles formed by the intersection of two lines. They are always congruent, meaning they have the same measure.

Given that ∠D and ∠F are vertical angles, we can equate their measures:

m∠D = m∠F

Since m∠D = (4x + 8)°, we can set it equal to m∠F:

4x + 8 = m∠F

Now substitute the value of ∠F from the given information, which states that ∠E and ∠D are supplementary:

m∠E + m∠D = 180°

Since m∠E = (x + 17)° and m∠D = (4x + 8)°, we can substitute these values into the equation:

(x + 17) + (4x + 8) = 180

Combine like terms:

5x + 25 = 180

Subtract 25 from both sides:

5x = 155

Divide both sides by 5:

x = 31

Now substitute x = 31 into the equation for ∠F:

4(31) + 8 = m∠F

124 + 8 = m∠F

m∠F = 132°

Therefore, the measure of ∠F is 132°.

In a geometric diagram, ∠A and ∠B are complementary, and they form a straight line with ∠C . If m∠A=x° , m∠B=(2x)° , and m∠C=90° , what is the measure of ∠B ?

180°
60°
30°
90°

In this scenario, ∠A and ∠B are complementary, meaning that their measures add up to 90°.

Given that the measure of ∠A is x°, we can write the equation:

m∠A + m∠B = 90°

Substituting the given values for ∠A and ∠B:

x° + (2x)° = 90°

Combining like terms:

3x° = 90°

Dividing both sides by 3:

x° = 30°

Therefore, the measure of ∠B is (2x)°, or (2*30)°, which equals 60°.