Question

Two angles differ by 90°.if one is 1/3 of the number,find the angles​

Answer 1

GIVEN :–

• Difference of two angles is 90°.

• One angle is ⅓ of second angle.

TO FIND :–

• Angles = ?

SOLUTION :–

• Let the the first angle is 'x' , then second angle is 'x/3'.

• According to the question –

$\\ \bf \implies x - \dfrac{x}{3} = {90}^{ \circ}$

$\\ \bf \implies \dfrac{3x - x}{3} = {90}^{ \circ}$

$\\ \bf \implies \dfrac{2x}{3} = {90}^{ \circ}$

$\\ \bf \implies 2x=3 \times {90}^{ \circ}$

$\\ \bf \implies 2x={270}^{ \circ}$

$\\ \bf \implies x= \dfrac{1}{2} \times {270}^{ \circ}$

$\\\large\implies{ \boxed{ \bf x={135}^{ \circ}}}$

• Other angle –

$\\\implies\bf \dfrac{x}{3}= \dfrac{{135}^{ \circ}}{3}$

$\\\large\implies{ \boxed{ \bf \dfrac{x}{3}= {45}^{ \circ}}}$

• Hence , First angle is 135° and second angle is 45°.

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VERIFICATION :–

• Difference between angles = 90°

=> 135° - 45° = 90°

=> 90° = 90°

[ Hence Proved ]

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Answer 2

♣GIVEN :–

• Difference between two angles = 90°

• One of the number is 1/3 of the other number

♣TO FIND :–

• The measure of the angles

♣SOLUTION :–

Let one of the angles be x °

ஃ The other one must be = (1/3 × x)° = (x/3)°

卐 By the problem :-

→ x + x/3 = 90 [It is stated that the difference of the angles is 90°]

→ 3x - x/3 = 90

→ 2x/3 = 90

→ 2x = 90 × 3

→ x = 270/2

➠ x = 135

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• The first angle = x° = 135°

• The other angle = (x/3)° = (135/3)° = 45°

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★ Let's Verify Our Result Now :–

• x + x/3 = 90

⟹ 135 - (135/3) = 90

⟹ 135 - 45 = 90

⟹ 90 = 90

LHS = RHS

HENCE VERIFIED!!