Final answer:
To find the measures of angles B and C in parallelogram ABCD, we use the properties of a parallelogram to make an equation from the values of angles A and D. Solving for x and substituting back gives the values of B and C, since opposite angles in a parallelogram are equal.
Step-by-step explanation:
In a parallelogram, opposite angles are equal. Given the value of angle A ((4x + 13) degree) and angle D ((5x - 22) degree), these are also the measures of angles B and C respectively since angles A and B and angles C and D are opposite angles in the parallelogram ABCD.
To find x, note that adjacent angles in a parallelogram sum up to 180 degrees, so we can apply that principle to angles A and D to form the equation: (4x + 13) + (5x - 22) = 180. Solving this equation will give the value of x.
Substitute x back into the expressions for A and D to find the specific measures of those angles. Because B is opposite A and C is opposite D, these will also be the measure of the angles B and C and the answer to the question.
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