Asked by bigepic

In the diagram, m∠A=(4x−10)° and m∠D=(2x+22)° . What is the measure of ∠D ?

(1 point)
Answered by bigepic
its 180
Answered by bigepic
wait actually its 90
Answered by bigepic
nvm both are wrong
Answered by bigepic
the answer is 54 but why is that
Answered by bigepic
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 ?
Answered by bigepic
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 ?
Answered by bigepic
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

Answered by GPT 3.5
We do not have enough information to determine the measure of angle D. We need to have the value of x in order to find the measure of angle D.
Answered by GPT 3.5
If angle A and angle D are supplementary, then their measures add up to 180 degrees. Therefore, we have the equation (4x - 10) + (2x + 22) = 180. We can solve this equation to find the value of x.

Combining like terms, we have 6x + 12 = 180.

Subtracting 12 from both sides, we get 6x = 168.

Dividing both sides by 6, we get x = 28.

Substituting x = 28 into the expression for angle D, we have 2x + 22 = 2(28) + 22 = 56 + 22 = 78.

Therefore, the measure of angle D is 78 degrees.
Answered by GPT 3.5
If angle A and angle D are complementary, then their measures add up to 90 degrees. Therefore, we have the equation (4x - 10) + (2x + 22) = 90. We can solve this equation to find the value of x.

Combining like terms, we have 6x + 12 = 90.

Subtracting 12 from both sides, we get 6x = 78.

Dividing both sides by 6, we get x = 13.

Substituting x = 13 into the expression for angle D, we have 2x + 22 = 2(13) + 22 = 26 + 22 = 48.

Therefore, the measure of angle D is 48 degrees.
Answered by GPT 3.5
I apologize for the incorrect information. If angle A is (4x - 10)° and angle D is (2x + 22)°, we can set up the equation:

(4x - 10) + (2x + 22) = 180

Combining like terms, we have:

6x + 12 = 180

Subtracting 12 from both sides, we get:

6x = 168

Dividing both sides by 6, we get:

x = 28

Now we can substitute x = 28 into the expression for angle D:

2x + 22 = 2(28) + 22 = 56 + 22 = 78

Therefore, the measure of angle D is 78 degrees.
Answered by GPT 3.5
Apologies for the previous incorrect response. Given that angle A is (4x - 10)° and angle D is (2x + 22)°, if the two angles are adjacent and form a straight line (180 degrees), we can set up the equation:

(4x - 10) + (2x + 22) = 180

Combining like terms, we have:

6x + 12 = 180

Subtracting 12 from both sides, we get:

6x = 168

Dividing both sides by 6, we get:

x = 28

Now we can substitute x = 28 into the expression for angle D:

2x + 22 = 2(28) + 22 = 56 + 22 = 78

The measure of angle D is 78 degrees, not 54 as previously stated. I apologize for the incorrect response.
Answered by GPT 3.5
If angles A, B, and C are angles whose measures add up to 180°, we can set up the equation:

m∠A + m∠B + m∠C = 180

Substituting the given measures, we have:

67 + (2x + 20) + x = 180

Combining like terms, we get:

3x + 87 = 180

Subtracting 87 from both sides, we have:

3x = 93

Dividing both sides by 3, we get:

x = 31

Now we can substitute x = 31 into the expression for angle B:

2x + 20 = 2(31) + 20 = 62 + 20 = 82

Therefore, the measure of angle B is 82°.
Answered by GPT 3.5
If angles D and E are supplementary, their measures add up to 180°. Therefore, we have the equation:

m∠D + m∠E = 180

Substituting the given measures, we have:

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

Combining like terms, we get:

5x + 25 = 180

Subtracting 25 from both sides, we have:

5x = 155

Dividing both sides by 5, we get:

x = 31

Now we can substitute x = 31 into the expression for angle D:

4x + 8 = 4(31) + 8 = 124 + 8 = 132

Therefore, the measure of angle D is 132°.

Since angle F is a vertical angle with angle D, it has the same measure as angle D. Therefore, the measure of angle F is also 132°.
Answered by GPT 3.5
If angles A and B are complementary, their measures add up to 90 degrees. Therefore, we can set up the equation:

m∠A + m∠B = 90

Substituting the given measures, we have:

x + 2x = 90

Combining like terms, we get:

3x = 90

Dividing both sides by 3, we get:

x = 30

Now we can substitute x = 30 into the expression for angle B:

2x = 2(30) = 60

Therefore, the measure of angle B is 60 degrees.