Question

In the figure, AC is diameter, angle A = 35°, the angle C is equal to

(A) 90° (B) 35° (C) 55° (D) 70°​

Answer 1

Answer:

110°

Step-by-step explanation:

Given that AC is the diameter of the circle,

Also, Given that ∠ADB = 20°,

Now, if we consider AB as the chord of the circle and the major segment

ADCB, we have

∠ACB = ∠ADB ( Angles in the same segment)

∠ACB =  20°.

Also,

∠ABC = 90°( Angle subtnded by the diameter of a circle)

Now, in triangle ABC,

∠ABC + ∠BCA +∠CAB = 180°

=> ∠CAB = 180° - 90° - 20°

=>∠CAB = 70°.

Now, consider the quadrilateral ACPB, we can observe that all the vertices

of the quadrilateral lie on the same circle, hence ACPB is a cyclic

quadrilateral.

We know that, in a cyclic quadrilateral opposite angles are supplementary

Hence, ∠CAB + ∠BPC = 180°

=>∠BPC = 180° - 70°

= 110°

Answer 2

The Value of Angle C = 55 degrees.

GIVEN: AC is diameter, angle A = 35°,
TO FIND: Value of Angle C
SOLUTION:

As we are given in the question,

BD is the diameter of the circle.

An angle in a semicircle is a right angle

∠BAD = 900

Consider ∠BAD

Using the angle sum property

∠ADB + ∠BAD + ∠ABD = 180°

By substituting the values

∠ADB + 90° + 35° = 180°

On further calculation

∠ADB = 180° - 90° - 35°

By subtraction

∠ADB = 180° - 125°

So we get

∠ADB = 55°

We know that,

The angles in the same segment of a circle are equal

∠ACB = ∠ADB = 55°

So we get

∠ACB = 55°

Therefore,

∠ACB = 55°

#SPJ2