Question

if the ratio of two complementry angles is 2:3, find them

Answer 1

Answer :- 36° and 54°

Explanation :-

Let the Two angle be 2x and 3x respectively,

We known that complementary angle = 90°

2x + 3x = 90° [ Adding 2x and 3x ]

5x = 90°

x = 90/5

x = 18

Therefore x = 18

Substituting x = 18

In both angle

2x

2(18)

= 36°

3x

3(18)

= 54°

Therefore, the two angles are 36° and 54°

Answer 2

$\mathfrak\pink{Solution}$

$\bold\red{What\:is\: complementary\: Angle}$

Complementary angle, refers to the sum of two angles say x and y, whose sums adds to be 90°. Such that x+y =90°

$\mathfrak\orange{Now,\: According\:to\:the\: question}$

Let the common ratio be x

Given ratios= 2x, 3x

Now,

$\mathfrak\green{We\:know\:that\:the\: sum\:of\: complementary\:angle\:is\:90°}$

Therefore,

2x+3x= 90°

$→5x = 90° \:$

$→x = \frac{90}{5}$

$→x = 18° \:$

Now,

$\mathfrak\red{Value\:of\:2x}$=2×18

=36°

$\mathfrak\orange{Value\:of\:3x}$=3×18

=54°

Now,

$\mathfrak\blue{Verification}$

$\bold{As,\:we\:know\;that \:the \:sum \:of \:angles \:is \:90°\:in\:case\:of\: complementary\:angles}$

Therefore,

2x+3x= 90°

$→ 36 + 54 = 90° \:$

$→90° = 90° \:$

Therefore,

LHS=RHS