Answer:
A = 45°, B = 135°, C = 45° and D = 135°,
Step-by-step explanation:
Kenneth building is in the shape of a parallelogram, ABCD.
Since, opposite angles of a parallelogram are equal,
A = C and B = D. --- (1)
Since, adjacent angles of a parallelogram are supplementary,
B + C = 180 --- (2)
But, it is given that the measure of angle C is one third of measure of angle B.
Therefore, [tex]C = \frac{1}{3} (B)[/tex] or
B = 3C
Substitute in (2), we get,
3C + C = 180
4C = 180
Divide both sides by 4.
C = 45°
B + C = 180
B + 45 = 180
B = 180 - 45
B = 135°
From (1),
A = C and B = D
Therefore, A = 45° and D = 135°
Hence, A = 45°, B = 135°, C = 45° and D = 135°,
