Question

in the given figure AO and DO are the bisectors of angle A and angle D of the quadrilateral ABCD find angle AOD

OPTIONS:
A.67.5
B.77.5
C.87.5
D.99.75

plz ans correctly according to these options

i will like your answer ​

Answer 1

Answer:

c . 87.5°

Step-by-step explanation:

ABCD is a quadrilateral

let ∠OAD and ∠ODA be x and y respectively.

∠OAD = ∠OAB = x

∴ ∠BAD = 2x

∠ODA = ∠ODC = y

∴∠ADC = 2y

sum of all angles in a quad = 180°

105 + 70 + 2x + 2y = 360°

175 + 2(x+y) = 360°

2 (x+ y) = 360 - 175

x+ y = 185/2

x + y = 92.5 ......... (i)

In ΔOAD :-

sum of all angles in a Δ = 180°

x + y +  ∠AOD= 180°

92.5 +∠AOD= 180°

∠AOD = 180 - 92.5

= 87.5

Answer 2

Given:

quadrilateral ABCD

∠C=105°  

∠B=70°

bisectors of ∠A, and ∠D

∠A+∠B+∠C+∠D=360°   [angle of quadrilateral ABCD]

2∠AOD=∠C+∠B

2∠AOD= 105° + 70°

2∠AOD = 175°

∠AOD = 175°/2

∠AOD  = 87.5

The correct option is "c"

Hence angle AOD is 87.5°