two supplementary angles are in the ratio of 2:7 find the angle
Answers
Solutions :-
Supplementary Angle
The two angles whose measure 180° is known as supplementary angles.
Your question ➠
Q:- Two supplementary angles are in the ratio of 2:7. Find the angle .
➠
Let the first angle be 2x
And second angle be 7x
We know,
The measure of two angles of supplementary angles is 180°.
A/q
=> 2x + 7x = 180°
=> 9x = 180°
=> x = 180°/9 = 20°
Hence,
First angle = 2x = 2 × 20° = 40°
Second angle = 7x = 7 × 20° = 140°
Greetings..!
Supplementary angles are two such angles that sum up to make 180°.For example 100° and 80° are supplementary angles because their sum is 180°.
Now,coming to the question ,
Let the common multiple of each term of ratio be x.
Then, ratio becomes 2x:7x
As , their sum should be 180°,
⇒2x + 7x = 180°
⇒9x = 180°
⇒x = 180 ÷ 9
⇒x = 20
So, the angles are ,
2x = 2 * x = 2*20 = 40°
7x = 7 * x = 7 * 20 = 140°
We can verify by adding them , as 140+40 = 180°
Answer : hence, the angles are 40° and 140°.