Question

In the adjoining figure, the diagonals AC and BD of parallelogram
ABCD intersect at 0. If ZOBC = 36°, ZODC = 28º and ZAOD = 64°;
find the measure of (i) ZOAD (ii) ZOCD.
28°
64°
36°
​

Answer 1

Answer:

Given: parallelogram ABCD

diagonal AC and BD intersect at O

LOBC=36°, LODC=28° and LOAD=64°

To prove: (I) LOAD and (ii) LOCD

Proof: since LOBC=36°

LOBC=LOAD ( Angle in same segment)

so LOAD=36°

Since, LAOD=64°

so LAOD+LDOC=180° (Linear pair)

64°+LDOC=180°

LDOC=180°-64°

LDOC=116°

Now in triangle DOC

LDOC+LODC+LOCD=180° (angle sum property)

116°+28°+LOCD=180°

144°+LOCD=180°

LOCD=180°-144°

LOCD= 36°

Therefore

LOAD=36°

LOCD=36°