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.
