Final answer:
To find the measure of angle B in parallelogram ABCD, we solve for x by setting the expressions for the opposite angles A and C equal to each other and then substitute x back into the expression. We find angle B by subtracting angle A's measure from 180 degrees since they are supplementary, resulting in a measure of approximately 164.25 degrees.
Step-by-step explanation:
To solve for the measure of angle B in a parallelogram ABCD, we use the properties of a parallelogram which state that opposite angles are equal. Given the measure of angle A as 3x+10 and the measure of angle C as 15x-13, we can set the two expressions equal to each other to find the value of x because in a parallelogram, angle A is equal to angle C.
3x + 10 = 15x - 13
We then solve for x:
10 + 13 = 15x - 3x
23 = 12x
x = 23 / 12
x = 1.9167 when rounded to four decimal places
Now, we substitute this value back into the expression for angle A or C to find the measure of one of the opposite angles:
Angle A = 3(1.9167) + 10
Angle A = 5.7501 + 10
Angle A = 15.7501 degrees when rounded to four decimal places
Since angle A and angle B are consecutive angles in a parallelogram and consecutive angles are supplementary, we subtract the measure of angle A from 180 degrees to find the measure of angle B:
Angle B = 180 - 15.7501
Angle B = 164.2499 degrees when rounded to four decimal places
Therefore, the measure of angle B is approximately 164.25 degrees.