Question

In parallelogram ABCD, angles A and C are opposite angles with the measure of angle

A as 6x+8 and the measure of angle C as 13x-13. What is the measure of angle B?
Answer as a decimal rounded to the nearest hundredth if not a decimal.
Your Answer:
Answer

Answer 1

By setting up an equation based on the fact that opposite angles in a parallelogram are equal, solving for x, and then using the measure of angle A to find angle B, we determine that the measure of angle B is 154 degrees.

In a parallelogram, opposite angles are equal. Therefore, we can set up an equation based on the given information about angles A and C:

Angle A = Angle C

6x + 8 = 13x - 13

Now, solve for x:

7x = 21

x = 3

Now that we know the value of x, we can find the measure of angle B. Angle B is adjacent to angle A, so we can use the measure of angle A to find angle B:

Angle B = 180 degrees - Angle A

Angle B = 180 degrees - (6(3) + 8)

Angle B = 180 degrees - 26

Angle B = 154 degrees

So, the measure of angle B in parallelogram ABCD is 154 degrees.