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 ?(1 point) Responses 62° 62 degrees 180° 180 degrees 31° 31 degrees 82°

5 answers

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

∠A + ∠B + ∠C = 180°

Substituting the given measures, we get:

67° + (2x + 20)° + x° = 180°

Combining like terms, we get:

3x + 87° = 180°

Subtracting 87° from both sides, we get:

3x = 93°

Dividing both sides by 3, we get:

x = 31°

So, the measure of ∠B is:

2x + 20 = 2(31) + 20 = 82°

Therefore, the correct answer 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 ? (1 point) Responses 48° 48 degrees 31° 31 degrees 132° 132 degrees 124°
To find the measure of ∠F, we need to find the value of x first. Since ∠D and ∠E are supplementary angles, their measures add up to 180°:

m∠D + m∠E = 180°

Substituting the given measures, we get:

(4x + 8)° + (x + 17)° = 180°

Combining like terms, we get:

5x + 25° = 180°

Subtracting 25° from both sides, we get:

5x = 155°

Dividing both sides by 5, we get:

x = 31°

Now that we know x = 31°, we can find the measure of ∠D:

m∠D = (4x + 8)° = (4 * 31 + 8)° = 124°

Since ∠F is a vertical angle with ∠D, they have the same measure. Therefore, the measure of ∠F is also 124°.

Therefore, the correct answer is 124°.
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 ?(1 point) Responses 60° 60 degrees 180° 180 degrees 90° 90 degrees 30°
Since ∠A and ∠B are complementary, their measures add up to 90°.

Therefore, we can set up the equation: ∠A + ∠B = 90°

Substituting the given measures, we get: x° + 2x° = 90°

Combining like terms, we get: 3x° = 90°

Dividing both sides by 3, we get: x° = 30°

Thus, the measure of ∠B is: 2x° = 2(30°) = 60°

Therefore, the correct answer is 60°.