5. Seg AB is the diameter of a circle. C is the point on the circumference such that in ∆ABC, ∠B is the less by 10º than ∠A. Find the measures of all the angles of ∆ ABC.

5. Seg AB is the diameter of a circle. C is the point on the circumference such that in ∆ABC, ∠B is the less by 10º than ∠A. Find the measures of all the angles of ∆ ABC.

Solution:

Let the measures of  ∠A be xº and measure of ∠B be yº.

Seg AB is the diameter of a circle and C is a point on the circumference.

∴ m ∠C = 90⁰

[∵ The angle subtended by a diameter at any point on the circle other than its end points is a right angle]

In ∆ ABC,

m ∠A + m ∠B + m ∠C = 180⁰  [∵ Sum of measures of the angles of a triangle is 180⁰]

∴  x + y + 90 = 180

∴ x + y = 180 – 90

∴  x + y = 90 ........eq. no. (1)

As the given condition,

∠ B = ∠ A – 10⁰

∴ y = x - 10

∴ x – y = 10 ......... eq. no. (2)

Adding equations (1) and (2)

x + y = 90

x – y = 10

2x     =  100

∴ x = 100/2

∴ x = 50

Substituting x = 50 in equation no. (1)

x + y = 90

∴ 50 + y = 90

∴ y = 90 – 50

∴ y = 40

The measures of angle of ∆ ABC are 50º, 40º and 90º.