Answer:
The angles of the deck are 45°, 135°, 45° and 135°.
Step-by-step explanation:
It is given that C is one third of measure of angle B.
But, in a parallelogram, adjacent angles are supplementary.
Therefore, B + C = 180
[tex]C=\frac{1}{3} B[/tex]
[tex]B=\frac{B}{3} =180[/tex]
[tex]\frac{4B}{3} =180[/tex]
[tex]B=180(\frac{3}{4} )[/tex]
B = 135
and [tex]C=\frac{135}{3}[/tex]
C = 45
Since, opposite angles are equal in a parallelogram,
A = C = 45 and
D = B = 135
Hence, the angles of the deck are 45°, 135°, 45° and 135°.
