Question

In a right triangle, the two smaller angles are in the ratio 1:4. Compute these angles

Answer 1

Given :

• Two smaller angles are in the ratio 1:4 .

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To Find :

• The angles = ?

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Solution :

$\dag \; {\underline{\pmb{\frak{ We \; know \; That \; :- }}}}$

In a Right angled triangle one angle is 90° .And the rest two angles are in the ratio 1:4 as we have been provided in the question .

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$\dag \; {\underline{\pmb{\frak{ Let \; the \; Ratios \; :- }}}}$

• ➟ ∠1 = 90°
• ➟ ∠2 = 1y°
• ➟ ∠3 = 4y°

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$\dag \; {\underline{\pmb{\frak{ Angle \; Sum \; property \; :- }}}}$

• ${\underline{\boxed{\red{\sf{ Sum \; of \; Angles{\small_{(Triangle)}} = 180° }}}}}$

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$\dag \; {\underline{\pmb{\frak{ Calculating \; the \; value \; of \; y \; :- }}}}$

${\dashrightarrow{\qquad{\sf{ ∠1 + ∠2 + ∠3 = 180° }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 90° + 1y° + 4y° = 180° }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 90° + 5y° = 180° }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 5y° = 180° - 90° }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 5y° = 90° }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ y = \dfrac{90}{5} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ y = \cancel\dfrac{90}{5} }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\pmb{\pink{\frak{ y = 18° }}}}}}}}$

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$\dag \; {\underline{\pmb{\frak{ Calculating \; the \; Angles \; :- }}}}$

• ➳ ∠2 = 1y = 1(18) = 18°
• ➳ ∠3 = 4y = 4(18) = 72°

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$\dag \; {\underline{\pmb{\frak{ Therefore \; :- }}}}$

❛❛ The other two angles are 18° and 72° . ❜❜

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