Question

in in the given figure, angle angle BAD = 65°, angle ABD = 70° and angle BDC =45° .
i) prove that AC is a a diameter of the circle
ii) find angle ACB ​

Answer 1

25°

Step-by-step explanation:

angle ADB = 180 - (65+70) = 45° so angle ADC = 45+45 = 90°

sum of opposite angles of quadrilateral= 180°

ADC + ABC = 180°

90 + ABC = 180 => ABC = 90°= ADC , hence AC is a diameter of the circle.

(ii) ACB = 180 - (65+ABC)

= 180 - (65+90°) = 25°

Answer 2

Answer:

angle A :65

angle A+angle C=180( sum of opposite angles in quadrilateral)

65+C=180

C= 180-65

=115

In ∆DCB,

45+115+B=180(sum of interior angles)

B=180-160

=20

So angle B (according to the quadrilateral)=90

Then, Angle B is 90.

so AC is the diameter (opposite angle is 90)

In∆DAB

65+70+D=180(sum of interior angles)

D=180-135

=45

Angle D is 45

so angle ACB will be 45 (angles on same segment AB)

Hence proved AC is a diameter and angle ACB is 45