Question

in the diagram, m<A : (4x - 20) a d m<D = (2x + 22). what is the measure of <D? They are supplementary so these number add up to 180.

Answer 1

in the diagram, m<A : (4x - 10) a d m<D = (2x + 22). what ks the measurr of <D

Answer 2

If angles A and D are supplementary, their measures add up to 180 degrees.
Therefore, we can write the equation:

(4x - 20) + (2x + 22) = 180

Simplifying this equation, we combine like terms:

6x + 2 = 180

Next, we isolate the variable by subtracting 2 from both sides:

6x = 178

Finally, we solve for x by dividing both sides by 6:

x = 29.67

Now that we have the value of x, we can substitute it back into either angle's measure to find the measure of angle D. Let's substitute it into angle D's measure:

m<D = 2(29.67) + 22 = 59.34 + 22 = 81.34

Therefore, the measure of angle D is approximately 81.34 degrees.

Answer 3

If angles A and D are supplementary, their measures add up to 180 degrees.
Therefore, we can write the equation:

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

Simplifying this equation, we combine like terms:

6x + 12 = 180

Next, we isolate the variable by subtracting 12 from both sides:

6x = 168

Finally, we solve for x by dividing both sides by 6:

x = 28

Now that we have the value of x, we can substitute it back into either angle's measure to find the measure of angle D. Let's substitute it into angle D's measure:

m<D = 2(28) + 22 = 56 + 22 = 78

Therefore, the measure of angle D is 78 degrees.