one angle of a triangle is equal to sum of other two angles. if the ratio between other two angles is 4 : 5. find all the angles?
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Given:
Ratio between two other angles is 4:5.
Let x be the common multiple of the ratio.
So, angle a = 4x
angle b = 5x
angle c = a + b = 4x + 5x = 9x
4x + 5x + 9x = 180
9x + 9x = 180
18x = 180
x =
x = 10
Substitute the values of x in the angles.
Angle a = 4x = 4 × 10 = 40°
Angle b = 5x = 5 × 10 = 50°
Angle c = 9x = 9 × 10 = 90°
According to the property of sum of all angles of a triangle is 180°,
angle a + angle b + angle c = 180°
40 + 50 + 90 = 180
90 + 90 = 180
180 = 180
Hence, verified.
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