In the diagram, m∠A=(4x−10)° and m∠D=(2x+22)° . What is the measure of ∠D ?
(1 point)
the answer is 54 but why is that
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 ?
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°.
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 ?
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°.
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
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.
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.
its 180
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.