2.
The ratio of measurements of two angles A and B of a triangle
2:3 whereas the ratio of measurements of angle C and angle B
1:3 calculate the measurement of each angle of that triangle?
Answers
Answer:
Correct option is
A
30
∘
,60
∘
,90
∘
Sum of angles of a triangle is 180
o
.
Given angles of a triangle are in ratio 1:2:3.
Let consider the angles as x, 2x and 3x respectively.
Hence,
x+2x+3x=180
o
=>6x=180
o
So, x=30
o
.
Hence other angles are 2x=60
o
and 3x=90
o
.
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Step-by-step explanation:
Given:-
The ratio of measurements of two angles A and B of a triangle is 2:3 whereas the ratio of measurements of angle C and angle B is 1:3.
To find:-
Calculate the measurement of each angle of that triangle?
Solution:-
Given that
The ratio of measurements of two angles A and B of a triangle = 2:3
∠A : ∠ B = 2 : 3
The ratio of measurements of angle C and angle B = 1:3
∠ C : ∠ B = 1:3
=> ∠ B : ∠ C = 3 :1
∠ A : ∠ B = 2 : 3
∠ B : ∠ C = 3 : 1
___________________
∠ A : ∠ B : ∠ C = 2 : 3 : 1
___________________
Let the angles be 2X° ,3X° and X°
Let ∠ A = 2X°
Let ∠ B = 3X°
Let ∠ C = X°
We know that
The sum of all angles in a triangle is 180°
=> 2X° + 3X° + X° = 180°
=> 6X° = 180°
=> X° = 180°/6
=> X° = 30°
and
3X°=3(30°)=90°
2X°=2(30°)=60°
∠ A = 60°
∠ B = 90°
∠ C = 30°
Answer:-
The measurements of the all angles in the given triangle are 60° , 90° and 30°
Used formula:-
Angle Sum Property:-
The sum of all angles in a triangle is 180°