Question

In parallelogram ABCD, angles A and C are opposite angles with the measure of angle A as 7x+8 and the measure of angle C as 10x-22. What is the measure of angle B? Answer as a decimal rounded to the nearest hundredth if not a decimal.

Your Answer:

Answer 1

The measure of angle B in parallelogram ABCD, using the given expressions for angles A and C, is found to be 102 degrees after solving for x and using the properties of a parallelogram.

Step-by-step explanation:

In parallelogram ABCD, we know that opposite angles are congruent, meaning that the measure of angle A is equal to the measure of angle C. We are given that the measure of angle A is 7x+8 and the measure of angle C is 10x-22. Since angles A and C are congruent, we can set their measures equal to each other to find the value of x:

1. 7x + 8 = 10x - 22
2. Subtract 7x from both sides: 8 = 3x - 22
3. Add 22 to both sides: 30 = 3x
4. Divide by 3: x = 10

Now that we have the value of x, we can find the measure of angle A or C by substituting x back into either equation:

• Measure of angle A = 7(10) + 8 = 70 + 8 = 78
• Measure of angle C = 10(10) - 22 = 100 - 22 = 78

Because angle B is adjacent to angle A in a parallelogram, angle B and angle A are supplementary, meaning their measures add up to 180 degrees:

• Measure of angle B = 180 - Measure of angle A
• Measure of angle B = 180 - 78 = 102