Question

8. ABCD is a quadrilateral in which the bisectors of angle B and angle C meet at O. If Angle A = 100°
and Angle D = 70°, find the measure of Angle BOC.​

Answer 1

Answer:

In quadrilateral ABCD

∠A = 100° ….. (given )

∠D = 70° ……. (given )

∠B=∠D= 70° …… [ opposite angles of quadrilateral (parallelogram) are equal]

∠A=∠C=100° …… [ opposite angles of quadrilateral (parallelogram)are equal]

A.T.Q.

∠B/2=70/2=35

∠C/2=100/2=50

In the triangle BOC

∠B+∠O+∠C = 180  [ANGLE SUN PROPERTY OF TRIANGLE ]

35+50+∠O = 180

75 + ∠O = 180

∠O = 180-75

∠O = 105°

HENCE ; ANGLE BOC = 105°

Step-by-step explanation:

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