Question

seg AB is the diameter of a circle. c is the point on the circumference such that in triangle ABC, angle B is less than by 1o degree than angle A . find the measure of all the angles of triangle ABC.

Answer 1

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.

Hope This Helps :)