Question

In the adjoining figure,
angle APB = 78°. Find angle ACB.​

Answer 1

∠ACB = 51°

Given

To find the ∠ACB = ?

From the figure,

Where AB is a diameter, O as a center and AT is tangent at ∠AOQ = 58°,

find ∠ATQ = ?

In ΔABT,

∠ABT = 1/2 × ∠AOQ

= 1/2 × 58°

∠ABT = 29°

To find ∠ATQ :

Where, ∠A = 90°   ;     ∠B = 29°

Sum of all the angle is 180°.

∠A + ∠B + ∠T = 180°

90° + 29° + ∠T = 180°

119° + ∠T = 180°

∠T = 180° - 119°

∠T = 61°

Hence, ∠ATQ = 61°.

Taking above problem as an example and finding value for ∠ACB.

Change the values for the figure to find the value of ∠ACB.

In the given figure,

Place AD instead of AB

Place P instead of O

Place DB instead of BQ

Place AC instead of AT

After placing the values,

AD is a diameter and P is the center.

∠APB = 78°

∠ACB = ?

In ΔADC,

∠ADC = 1/2 × ∠APB

          = 1/2 × 78°

 ∠ADC = 39°

To find ∠ADC :

Where,  ∠A = 90°  and   ∠D = 39°

Sum of all the angles is 180°

∠A + ∠D + ∠C = 180°

90° + 39° + ∠C = 180°

129° + ∠C = 180°

          ∠C = 180° - 129°

           ∠C = 51°

Hence, ∠ACB = 51°.

To learn more...

brainly.in/question/5730504