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Question
In triangle ABC, the measure of ∠B is two-third of the measure of ∠A. The measure of ∠C is 20° more than the measure of ∠A. Find the measures of the three angles.
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Solution
Let angle ∠A be a°
Given that ∠B = `2/3 xx ∠"A" = 2/3"a"`
and given ∠C = ∠A + 20 = a + 20
Since A, B and C are angles of a triangle, they add up to 180° ...(∆ property)
∴∠A + ∠B + ∠C = 180°
⇒ `"a" + 2/3"a" + "a" + 20` = 180°
`(3"a" + 2"a" + 3"a")/3 + 20` = 180°
`(8"a")/3` = 180 – 20 = 160
∴ a =`(160 xx 3)/8` = 60°
∠B = `2/3 xx ∠"A" = 2/3 xx 60` = 40°
∠C = 80°
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