Lines and Angles Test

Result

Lines and Angles Test - 12

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0

In ΔABC, ∠A − ∠C = 27° and ∠C + ∠B = 104°. What is the sum of ∠A and ∠C?

A
55°

B
76°

C
125°

D
131°

Solution

It is known that the sum of all angles of a triangle is 180°.

∴ ∠A + ∠B + ∠C = 180° ... (1)

It is given that:

∠A − ∠C = 27° ... (2)

∠C + ∠B = 104° ... (3)

Adding equations (2) and (3):

∠A + ∠B = 131° … (4)

From equations (1) and (4):

∠C = 180° − 131° = 49°

From equation (3): ∠B = 104° − 49° = 55°

From equation (4): ∠A = 131° − 55° = 76°

∴ ∠A + ∠C = 76° + 49° = 125°

Thus, the sum of ∠A and ∠C is 125°.

The correct answer is C.