one side of a triangle is produced and the exterior angle so formed is 140°.If the corresponding interior opposite angles are in the ratio 3:4,find the measure of all the angles of the triangle.
answer is 60°,40°,80°
please solve....
Answers
Calculation of three interior angles of triangle
Answer: three interior angles of the triangle are 60° , 80° and 40°.
Explanation:
given that exterior angle of triangle = 140°
lets assume three angles of triangle be ∠ 1 , ∠2 and ∠3
let ∠ 1 , ∠2 be interior opposite angle to exterior angle of 140°.
As interior opposite angles are in ratio 3 : 4 ,
lets assume ∠ 1 = 3y and ∠2 = 4y.
Now we will be using following theorem to calculate two interior opposite angles
Theorem says "Sum of interior opposite angles of triangle is equal to an exterior angle"
=> ∠ 1 + ∠2 = exterior angle
=> 3y + 4y = 140°
=> 7y = 140°
=> y = 140/7 = 20
∠ 1 = 3y = 3 x 20 = 60°
∠2 = 4y = 4 x 20 = 80°
using angle sum property of triangle we can say that
∠ 1 + ∠2 + ∠3 = 180°
=> 60 + 80 + ∠3 = 180°
=> ∠3 = 180 - 140 = 40°
hence three interior angles of the triangle are 60° , 80° and 40°.
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Answer:
60 degree , 80 degree
Step-by-step explanation:
3x + 4x = 140degree
7x = 140 degree
x = 140/7 = 20 degree
angle 1 = 3x = 3 * 20 = 60 degree
angle 2 = 4x = 4 * 20 = 80 degree