In the figure two circles intersect at D. Angle BCD = 80 degree, Angle EFG = 70 degree. what is the measure of angle BAD? what is the measure of angle EDG?
Answers
Answer:
Given,
∠BAD=70
∘
, ∠ABD=56
∘
and ∠ADC=72
∘
.
ABCD is a cyclic quadrilateral.
We know, the sum of opposite angles of a cyclic quadrilateral is 180
o
.
Therefore,
∠BAD+∠BCD=180
∘
∠BCD=180
∘
−∠BAD
∠BCD=180
∘
−70
∘
=110
∘
Also, ∠ADC+∠ABC=180
o
72
∘
+(56
∘
+∠CBD)=180
∘
∠CBD=180
∘
−128
∘
=52
∘
.
In △BCD,
∠BCD+∠DBC+∠BDC=180
...[Angle sum property]
110
+52
+∠BDC=180
∠BDC=18
Answer:
BAD=70
∘
, ∠ABD=56
∘
and ∠ADC=72
∘
.
ABCD is a cyclic quadrilateral.
We know, the sum of opposite angles of a cyclic quadrilateral is 180
o
.
Therefore,
∠BAD+∠BCD=180
∘
∠BCD=180
∘
−∠BAD
∠BCD=180
∘
−70
∘
=110
∘
(i).
Also, ∠ADC+∠ABC=180
o
72
∘
+(56
∘
+∠CBD)=180
∘
∠CBD=180
∘
−128
∘
=52
∘
(ii).
In △BCD,
∠BCD+∠DBC+∠BDC=180
∘
Angle sum property]
110
∘
+52
∘
+∠BDC=180
∘
∠BDC=18
∘
.(i).