Question

an exterior angle of a triangle is 130 degree and one of the interior opposite angle is 45 degree find the other two angles of a triangle

Answer 1

let one angle= x
we know that sum of interior opposite angle = exterior angle
x+ 45 = 130
x = 130-45
x = 85
let another (3rd) angle= y
x+y+45= 180 ( sum of angles of triangle =180)
85 + y +45=180
130 + y=180
y = 180-130
y = 50

Answer 2

Answer:

85° and 50°

Step-by-step explanation:

Given:- Exterior angle of a triangle = 130°

            One of the opposite interior angle = 45°.

To find:- The other two angles of the given triangle.

Solution:-

As we know, Property of a triangle says that Exterior angle of a triangle is equal to sum of opposite interior angles.

In the given figure, In triangle ABC,

∠ACD = ∠ABC + ∠BAC          (from the given property.)

⇒ 130° = 45° + ∠BAC

⇒ ∠BAC = 130 - 45

⇒ ∠BAC = 85°

As we know, Sum of all the angle of a triangle is always 180°.

∴ ∠ABC + ∠BAC + ∠ACB = 180°

⇒ 45° + 85° + ∠ACB = 180°

⇒ ∠ACB = 180° - 45° - 85°

⇒ ∠ACB = 135° - 85°

⇒ ∠ACB = 50°

Therefore, Other two angles of the triangle are 85° and 50°.

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