Question

Set AB is is the diameter of a circle .C is the point on the circumference such that in∆ ABC ,/_B is less by10° than /_ A . Find the measures of all angles​

Answer 1

Answer:

Hey...

The answer to your question is as follows:

Step-by-step explanation:

Let angle A = x°

Therefore, angle B = x°-10°

In the circle ,

AB is the diameter.

C is a point on the circumference of the circle.

Therefore angle ACB = 90° ( ∵ angle in a semicircle is of 90° , here the semicircle is formed on diameter AB)

∴ In ΔACB ,

∠A + ∠B + ∠C = 180° ( Angle Sum Property of a Triangle )

putting the values of angles as,

∠A = x°

∠B = x° - 10°

∠C = 90°

∴ x° + x° - 10° + 90° = 180°

= 2x° = 180° - 90° + 10°

= 2x° = 100°

= x° = 50°

∴ ∠A = 50°

∠B = 50° - 10°

     = 40°

∠C = 90°

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I hope this clears your doubt.

Smile Please :)