An angle is equal to one-third of its supplement. The measure of angle is.

124

^{\circ}

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^{\circ}

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^{\circ}

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100

^{\circ}

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Solution

The correct option is C 45 $^{\circ}$
Let the measure of the required angle be $x$ .

Then, supplement of $x$ = $180^{\circ} - x$

It is given that,

$Angle = \frac{1}{3} (Supplement of x)$

$\Rightarrow x = \frac{1}{3} (180^{\circ} - x)$

$\Rightarrow 3 x = 180^{\circ} - x$

$\Rightarrow 4 x = 180^{\circ}$

$\Rightarrow x = 45^{\circ}$

Thus, the measure of the given angle is 45 $^{\circ}$ .

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Similar questions

Q. An angle is equal to two-third of its supplements. Find its measure.

The sum of an angle and one third of its supplementary angle is $90^{\circ}$ . The measure of the angle is
(a) $135^{\circ}$
(b) $120^{\circ}$
(c) $60^{\circ}$
(d) $45^{\circ}$

Find the measure of an angle which is equal to its supplement.

Q. The measure of an angle is

45^{\circ}

. The measures of its complement and supplement are respectively ___.

Find the measure of an angle which is

(i) equal to its complement,

(ii) equal to its supplement.

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An angle is equal to one-third of its supplement. The measure of angle is.

The correct option is C 45∘Let the measure of the required angle be x. Then, supplement of x = 180∘−x It is given that, Angle=13(Supplement of x) ⇒x=13(180∘−x) ⇒3x=180∘−x ⇒4x=180∘ ⇒x=45∘ Thus, the measure of the given angle is 45∘.