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What is the value of each angle of the triangle if the sum of two angles of a triangle is $116 °$ and their difference is $24 °$ ?

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75 °, 49 °, 55 °

70 °, 46 °, 64 °

65 °, 39 °, 64 °

69 °, 46 °, 79 °

answer is B.

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Detailed Solution

Given that the sum of two angles of a triangle is

116 °

and their difference is

24 °

.
Considering the given figure,
Question Image

Let us assume

△ A B C

and let

∠ A

∠ B

and

∠ C

to be the three angles of this triangle. Then according to question,

∠ A + ∠ B = 116 °

------------------(1)

∠ A − ∠ B = 24 °

------------------(2)
Subtracting equation (2) from (1),

∠ A + ∠ B − ∠ A − ∠ B = 116 ° − 24 ° 2 ∠ B = 92 ° ∠ B = 46 °

From equation (1),

∠ A − 46 ° = 24 ° ⇒ ∠ A = 24 ° + 46 ° ⇒ ∠ A = 70 °

The sum of interior angles of a triangle is

180 °

.
Now determining the value of

∠ C

by substituting values of

∠ A

and

∠ B

∠ A + ∠ B + ∠ C = 180 ° 70 ° + 46 ° + ∠ C = 180 ° ∠ C = 180 ° − 116 ° ∠ C = 64 °

Therefore, the measure of each angle of the triangle is

70 °, 46 ° and 64 °

.
Hence, option (2) is correct.

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