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.

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