Question

An exterior angle of a triangle measures 110 degree and its interior opposite angles are in the ratio 1:4. Find the angles of the triangle.

Answer 1

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Let the interior angles be x and 4x

ATQ

$x + 4x = 110$

$5x = 110$

$x = \frac{110}{5}$

$x = 22$

So the angles are 22 and 88.

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Answer 2

Given

• Exterior angle of triangle = 110°
• Interior opposite angles in ratio = 1:4

To find

• Angles of the triangle

Solution

As we know that

★ The sum of interior opposite angle is equal to exterior angle

Let the angle be x and 4x of the triangle

→ x + 4x = 110

→ 5x = 110

→ x = 110/5

→ x = 22

Hence,

• Angles :
• First angle = x = 22°
• Second angle = 4x = 22 × 4 = 88°

★ Sum of three angles of triangle is equal to 180°

Third angle = 180 - (22 + 88) = 70°

Therefore

• Third angle = 70°