Question

In a triangle largest angle is 20 degree more than the smallest angle . The third angle is 10 degree more than the smallest angle .



a) What is the sum of the angles in a triangle ?


b) What are the measures of the angles ?

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Answer 1

Answer :

a) Sum of three angles is 180°.

b)The measures of the triangle are 70° , 50° and 60° respectively.

Given :

• In a triangle, largest angle is 20° more than the smallest angle.
• The 3rd angle is 10° more than the smallest angle.

To find :

• a) What's the sum of the angles in a triangle ?
• b) What are the measures of the angles ?

Solution :

Consider,

• 1st angle (largest angle) = x°
• 2nd angle (smallest angle) = y°
• 3rd angle = z°

★ In a triangle, largest angle is 20° more than the smallest angle.

→x = y+20°....................(i)

★ The 3rd angle is 10° more than the smallest angle.

→ z = y+10°....................(ii)

We know that,

The sum of three angles of a triangle is 180°.

According to the question,

x + y + z = 180

• Put values.

→ (y +20) + y +( y + 10) = 180

→ 3y +30 = 180

→ 3y = 180-30

→ 3y = 150

→ y = 50

Therefore,

★ 2nd angle = 50°

★ 1st angle = 50°+20° = 70°

★ 3rd angle = 50°+10° = 60°

Then,

Sum of three angles ,

= 50°+70°+60°

= 180°

Therefore, sum of three angles is 180°.

Answer 2

a)

The sum of the angles in a triangle is 180

b) Given ,

• The largest angle of triangle is 20 degree more than the smallest angle

• The third angle is 10 degree more than the smallest angle

Let ,

• The smallest angle be ' x '

• Then , Largest angle = x + 20

• Third angle = ' x + 10 '

We know that ,

The sum of the angles in a triangle is 180

Thus ,

x + x + 20 + x + 10 = 180

3x + 30 = 180

3x = 150

x = 150/3

x = 50

$\therefore$ The measures of the angles of triangle are 50 , 70 and 60