Question

An exterior angle of a triangle is 80° and the interior opposite angles are in the ratio 1 : 3, measure of interior opposite angles are​

Answer 1

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An exterior angle of a triangle is 80° and the interior opposite angles are in the ratio 1 : 3 , measure of interior opposite angles are ?

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40° and 60°

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Given :-

• An exterior opposite angle of 80°

• And interior angles in ratio 1 : 3

To find :-

• The interior opposite angles

Property used :-

• Exterior angle property

Formula :-

• 80 = sum of interior opposite angles

Solution:-

Let the angles in ratio be 1x : 3x

So , by exterior angle property

• 80 = 1x + 3x

• 80 = 4x

• 80/4 = x

• 20 = x

• So , we get x = 20

• 3x = 3 (20) = 60

Check :-

• 20 + 60 = 80

• 80 = 80

So , the angles are 20° and 60°

Exterior Angle Property :-

• It is the property where the exterior angle is equal to the sum of two interior opposite angles.

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Similar question :-

The exterior angle of a triangle is 180° and the interior opposite angles are equal. Find the interior opposite angles.

Solution :-

Given :-

• Exterior angle = 180°

• Interior opposite angles are equal

To find :-

• The interior opposite angles

Solution :-

• Let both the interior opposite angles be x as they are equal.

So , by using exterior angle property ,

• x + x = 180°

• 2x = 180°

• x = 90°

Check :-

• 90 + 90 = 180

• 180 = 180

So , both the interior opposite angles are of 90.

Answer 2

Given

• An exterior angle of a triangle is 80° and the interior opposite angles are in the ratio 1 : 3

We Find

• Measure of interior opposite angles

We Know that

☆Sum of the Angels = 360 degree

☆Let The X :-

• Let the 1 be x = x

• Let the 3 be x = 3x

We Used

• Exterior Angle property

According to the question

( As, We used Exterior Angle property )

= x + 3x = 80°

= 4x = 80°

= x = 80°/4

= x = 20°

So, We Find values of Given X

X = 20° × 1 = 20°

3X = 20° × 3 = 60°

So, x is 20° and 3x is 60°

Verification

Exterior Angle = Sum of interior angle

80° = 20° + 60°

80° = 80°

So, That clear is x is 20° and 3x is 60°

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