The three angles of a triangle are in the ratio 1.2.1. find all the angles of the triangle
Mathematics
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Step-by-step solution
4 stepsLet the three angles of the triangle be A, B, and C.
The ratio of the angles is given as 1:2:1.
We can represent the angles as multiples of a common factor, say x.
Set up the angles based on the ratio.
Angle A = 1x
Angle B = 2x
Angle C = 1xUse the property that the sum of angles in a triangle is 180°.
A + B + C = 180°
1x + 2x + 1x = 180°Combine like terms and solve for x.
4x = 180°
x = 180° / 4
x = 45°Calculate the measure of each angle.
Angle A = 1x = 1 × 45° = 45°
Angle B = 2x = 2 × 45° = 90°
Angle C = 1x = 1 × 45° = 45°The three angles of the triangle are 45°, 90°, and 45°.
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