Question

the sum of an angle and one third of its supplementary angle is 90 .the measure of the angle is

Answer 1

$\textbf{Given:}$

$\textsf{The sum of an angle and one third of its}}$

$\textsf{supplementary angle is}\;\mathsf{90^\circ}$

$\textbf{To find:}$

$\textsf{Measure of the angle}$

$\textbf{Solution:}$

$\textsf{Let the required angle be}\;\mathsf{\theta}$

$\textsf{Then, its supplementary be}\;\mathsf{180^\circ-\theta}$

$\textsf{As per given data,}$

$\mathsf{\theta+\dfrac{1}{3}(180^\circ-\theta)=90^\circ}$

$\mathsf{\dfrac{3\theta+180^\circ-\theta}{3}=90^\circ}$

$\mathsf{\dfrac{2\theta+180^\circ}{3}=90^\circ}$

$\mathsf{2\theta+180^\circ=270^\circ}$

$\mathsf{2\theta=270^\circ-180^\circ}$

$\mathsf{2\theta=90^\circ}$

$\mathsf{\theta=\dfrac{90^\circ}{2}}$

$\implies\boxed{\mathsf{\theta=45^\circ}}$

$\textbf{Answer:}$

$\mathsf{The\;required\;angle\;is\;45^\circ}$

$\textbf{Find more:}$

Two complementary angles differ by 14 degree. What is the larger angle.

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