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 = 90x – y = 102x     =  100∴ x = 100/2∴ x = 50Substituting 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.

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