Question

One angle and its complementary are in the ratio of 2:3. Find the value of the angle please i will givw 11 points!!

Answer 1

Given : One angle and it's complementary are in the ratio 2 : 3

To Find : Value of those two angles.

As we know that :

• Sum of two complementary angles is 90°

Solution :

Put k in the ratio

Angles :

• 2k
• 3k

Now,

$\tt:\implies \: 2k + 3k = 90\degree$

$\tt:\implies \: 5k = 90\degree$

$\tt:\implies \: k = \cancel\dfrac{90}{5}$

$\tt:\implies \: k =\boxed{\boxed{\tt\purple{k = 18\degree}}}\bigstar$

Now,

• 2k = 2(18) = 36°
• 3k = 3(18) = 54°

$\sf\therefore{\underline{Hence, \: the \: angles \: are \: 36\degree \: and \: 54\degree \: respectively.}}$

Answer 2

${\underline{\underline{\bf{Given:}}}}$

• Two complementary angles are in the ratio 2 : 3.

${\underline{\underline{\bf{Need\:to\:find:}}}}$

• The measure of two angles.

${\underline{\underline{\bf{Concept:}}}}$

Complementary angles: A pair of angles whose sum is 90°.

${\underline{\underline{\bf{Solution:}}}}$

Let,

$\:\:\:\:\bullet{\sf{\:\angle A\:be\:2x}}$

$\:\:\:\:\bullet{\sf{\:\angle B\:be\:3x}}$

In case of complimentary angles,

$\longrightarrow{\sf{\angle A + \angle B = 90\degree}}$

$\:\:\:\:\:\implies{\sf{2x+3x=90}}$

$\:\:\:\:\:\implies{\sf{5x=90}}$

$\:\:\:\:\:\implies{\sf{x=\Large{\frac{\cancel{90}}{\cancel{5}}}}}$

$\:\:\:\:\:\implies{\underline{\underline{\sf{x=18}}}}$

We've obtained the value of $\sf{x}$. So, now we can substitute the value of x in the expressions formed for $\sf{\angle A}$ and $\sf{\angle B}$.

• $\bf{\angle A}$$\sf{\rightarrow 2x=2\times 18=\red{\underline{\underline{36\degree}}}}$
• $\bf{\angle B}$$\sf{\rightarrow 3x=3\times 18=\red{\underline{\underline{54\degree}}}}$

${\underline{\underline{\bf{Verification:}}}}$

$\rightarrow{\sf{Sum\:of\:two\:angles=90\degree}}$

$\rightarrow{\sf{\angle A+\angle B=90\degree}}$

$\rightarrow{\sf{36\degree+54\degree=90\degree}}$

$\rightarrow{\sf{90\degree=90\degree}}$

$\rightarrow{\sf{L.H.S=R.HS}}$

$\rightarrow{\sf{Hence,\:the\:answer\:is\:correct!}}$

${\underline{\underline{\bf{Required\:answer:}}}}$

• The measure of two complementary angles are 36° and 54°.

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