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In the given figure, two opposite angles of a parallelogram PQRS are (3x - 4)° and (56 - 3x)°. What is the value of the largest angle?

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124°

134°

144°

154°

answer is D.

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Detailed Solution

Given, in the given figure, two opposite angles of a parallelogram PQRS are (3x - 4)° and (56 - 3x)°.
Question Image

Opposite angles of a parallelogram are equal.

\Rightarrow

3x - 4 = 56 - 3x

\Rightarrow

6x = 60

\Rightarrow

x = 10°
So, 3x - 4 = 3(10) - 4 = 26°.
Thus, ∠P = ∠R = 26°.
The sum of adjacent angles in a parallelogram is 180°.

\Rightarrow

∠P + ∠S = 180°

\Rightarrow

26° + ∠S = 180°

\Rightarrow

∠S = 154°
The angles are ∠P = ∠R = 26°, ∠S = ∠Q = 154°.
So, the largest value of angle is 154°.
Hence, option 4 is correct.

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