3. A) The measures of two complement angles are x and
(x+50). Find the angles.
B) The three angles of a triangle are in the ratio 1:3:5. Find
all the angles of the triangle.
Answers
Question- 1 :-
SOLUTION :-
Given :-
Measure of two angles is complement the angles are
x,(x + 50)
To find :-
The angles
Solution:-
As we know that sum of two complement angles is 90° So,
x + (x + 50) = 90°
Open the brackets
x + x + 50 = 90°
2x + 50° = 90°
2x = 90°-50°
2x = 40°
x = 20°
Finding angles :-
x = 20°
x + 50° = 20°+50°
x+ 50° = 70°
Required angles are:-
20°,70°
Verification:-
So , sum of two angles must be 90° as they are complementary angles
20° +70° = 90°
90°=90°
Verified !
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QUESTION :- 2
Given :-
Three angles are in ratio 1:3:5
To find :-
Measure of two angles
Solution:-
As we know sum of two angles is 180° So,
- Let angles be 1x , 3x, 5x
1x + 3x + 5x = 180°
9x = 180°
x = 20°
Finding angles
x = 20°
3x = 3(20)
3x = 60°
5x = 5(20)
5x = 100°
Required angles are :- 20°,60°,100°
Verification:-
Therefore sum of those angles must be 180°
20°+60°+100° =180°
180°=180°
Hence verified
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1. Given :
- The measures of two complement angles are x and (x + 50)
To find :
- Find the angles.
Solution :
- In the question Complementary angles are given and we know that sum of complementary angle is 90°.
➤ x + (x + 50) = 90
➤ x + x + 50 = 90
➤ 2x = 90 - 50
➤ 2x = 40
➤ x = 40/2
➤ x = 20
Required angles are :
✰ x = 20°
✰ x + 50 = 70°
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2.Given :
- The three angles of a triangle are in the ratio 1:3:5.
To find :
- Find all the angles of the triangle.
Solution :
- Let the angles be 1x, 3x and 5x and we know that sum of all angles of triangle is 180°
➤ 1x + 3x + 5x = 180°
➤ 9x = 180°
➤ 9x = 180
➤ x = 180/9
➤ x = 20°
Required angles are :
✰ x = 20°
✰ 3x = 60°
✰ 5x = 100°
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