Question

Magnitude of an angle which is 2/3 of its supplement?Please answer fast.

Answer 1

Answer:

108

Step-by-step explanation:

2x/3=(180-x)

2x=360-3x

5x=360

x=72

(180-x) =180-72=108°

Answer 2

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✺Answer:

♦️GiveN:

• Magnitude of an angle is 2/3 of its supplement.

♦️To FinD:

• The magnitude of the angle...?

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✺Explanation of Q.

The question is based on the concepts of lines and angles in which we have to find unknown angles according to given condition. As mentioned in the question, supplementary angles, Let know something about Complementary and supplementary angles,

• Complementary angles

When two angles(magnitude of two angles) add upto 90°, then they are known as supplementary angles.

• Supplementary angles

When two angles add upto 180°, they are known to be as supplementary angles.

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Here, we use the concept of Supplementary angles.

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✺Solution:

Let the supplement angle be x

Then, the angle will be 2x/3

We know, supplementary angles add upto 180°, Using this we will solve it.

By using concept,

$\large{ \rm{ \rightarrow \: x + \frac{2x}{3} = 180}} \\ \\ \large{ \rm{ \rightarrow \: \frac{3x + 2x}{3} = 180}} \\ \\ \large{ \rm{ \rightarrow \: \frac{5x}{3} = 180}} \\ \\\large{ \rm{ \rightarrow \: x = \cancel{ \frac{180 \times 3}{5}}}} \\ \\ \large{ \rm{ \rightarrow \: x = \boxed{ \red{108}}}} \\ \\ \large{ \rm{ \rightarrow \: \frac{2x}{3} = \frac{2}{3} \times 108 = \boxed{ \red{72}}}} \\ \\ \large{ \therefore{ \underline{ \rm{ \purple{The \: angle \: is \: 72 \: and \: its \: supplement \: is \: 108}}}}}$

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