Question

Two supplementary angle are in ratio 4:5 find angles


and friend this question answer is 45⁰,45⁰ but you explain more answer this question ​

Answer 1

Given :

• The ratio of two supplementary angles = 4 : 5.

To Find :

• The two supplementary angles.

How to solve ?

• Given that, the ratio of two supplementary angles. We assume the both angles be 4x and 5x. First, we need to find the value of x then, we have to find the both supplementary angles by the help of the value of x. I.e., we obtain, the value of x is 20°. By the help of the value of x. We get the measure of both angles. I.e., the first angle is 4x, we substitute the value of x in the first angle "4x" and multiple both the numbers. So, the first angle is 80°. Same we can find the second supplementary angle, so the second angle be 5x, we have the value of x. So the second angle is 100°.
• For verify our answer : we have to add the both supplementary angles which we already found above. So we have, the first angle and the second angle are 80° and 100°. We add the both angles 80° and 100°. If we get 180° as the sum of both the angles then, our answer is absolutely correct.

Solution :

Let,

The first supplementary angle be 4x.

The second supplementary angle be 5x.

We know that,

The sum of two supplementary angles is 180°.

That means,

• First angle + Second angle = 180°

⇒ 4x + 5x = 180°

⇒ 9x = 180°

⇒ x = 180° / 9

⇒ x = 20°

Hence, the value of x is 20°.

So, the two supplementary angles are :

★ The first supplementary angle = 4x = 4 × 20° = 80°

★ The second supplementary angle = 5x = 5 × 20° = 100°

Hence,

The two supplementary angles are 80° and 100°.

Verification :

The sum of two supplementary angles is 180°

That means,

• First angle + Second angle = 180°

Now we have,

• First angle = 80°
• Second angle = 100°

⇒ 80° + 100° = 180°

⇒ 180° = 180°

Hence Verified !

Answer 2

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: Question :- \: \star}}}}}$

Two supplementary angle are in ratio 4:5 find angles.

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

Two supplementary angles are 80° and 100°.

$\Large{\underline{\underline{\bf{GiVen:-}}}}$

❥ Ratio of two supplementary angles ↠ 4 : 5.

$\Large{\underline{\underline{\bf{FiNd:-}}}}$

What are the values of these two supplementary angles ?

So , Here we go !

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

So we Let,

The first supplementary angle be 4x .

The second supplementary angle be 5x.

Sum of two supplementary angles is 180°.

As per this ,

• First angle + Second angle = 180°

↠ 4x + 5x = 180°

↠ 9x = 180°

↠ x = 180° / 9

↠ x = 20°

Hence, the value of x is 20°.

Now the putting the value of x

So, the angles are :

❥ First angle

↠ 4x = 4 × 20°

↠ 80°

❥ Second angle

↠ 5x = 5 × 20°

↠ 100°

Now checking or verifying :--

As we know ,

The sum of two supplementary angles is 180°

Now we got ,

↠First angle as 80°. and

↠ Second angle as 100°

↠ 80° + 100° = 180°

↠ 180° = 180°

Therefore ,

LHS = RHS

Proved !

$\mathfrak{\huge{\purple{\underline{\underline{Hence}}}}}$

❥ The two supplementary angles are 80° and 100°.

$\Large{\underline{\underline{\bf{Additional Information :-}}}}$

✮ What is supplementary angle ?

Two Angles are Supplementary when they add up to 180 degrees. They don't have to be next to each other, just so long as the total is 180 degrees.

Examples: 93° and 87° are supplementary angles.

✮ What is complementary angle ?

Two Angles are Complementary when they add up to 90 degrees (a Right Angle). They don't have to be next to each other, just so long as the total is 90 degrees.

Examples: 15° and 75° are complementary angles.

✮ What is adjacent angle ?

The two angles are said to be adjacent angles when they share the common vertex and side.

Note !

↠ Adjacent angles can be a complementary angle or supplementary angle when they share the common vertex and side.

✮ What is Vertical angle ?

Vertical angles are defined as the angles opposite to each other when two lines cross (i.e. intersect). It is also known as vertically opposite angles. It should be noted that two vertical angles are always equal.