The three angles of a triangle ABC are in the ratio 1:2:1.Find all the angles of the triangle .Classify
the triangle in two different ways.
Answers
Answer:
Let the angles be x, 2x, x.
∠A + ∠B + ∠C = 180° (Sum of all angles a triangle in 180°)
x + 2x + x = 180°
4x = 180°
x =
x = 45°
Measure of ∠A = 45°
Measure of ∠B = 2 × 45° = 90°
Measure of ∠C = 45°
The triangle is isosceles right angled triangle.
❍ Let the angles of the traingle be x, 2x and x respectively.
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Angle Sum Property of Triangle is basically, sum of all angles of the triangle is 180°.
Therefore,
Hence,
First angle, x = 45°
Second angle, x = 45°
Third angle, 2x = 2(45)° = 90°
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C L A S S I F Y I N G :
Here, we can see that Triangle has two equal angles, (45° and 45°). Therefore, the triangle is an isosceles triangle. (Isosceles triangle has two equal angles).
And, In the given triangle one angle is equal to 90° also. Therefore, the triangle is right – angled triangle.