Question

In a triangle largest angle is 20 degree more than the smallest angle. 3rd angle is 10 degree more than the smallest angle what is the sum of the angles in that triangle and what are the measures of the angles​

Answer 1

Answer:

the sum is 180° and measure of each angle is 50°,70° and 60°

Step-by-step explanation:

The theorm says that the sum of all the angles in a triangle is 180°

According to the given conditions:

let the smallest angle be x ......... eq 1

therefore, the largest angle will be

20+x ....... eq 2

and,

the 3rd angle will be

10+x ..........eq 3

adding all the equations we get

20+x+10+x+x= 180°

therefore x = 50°

largest angle = 70°

3rd angle = 60°

Answer 2

$\color {red} </p><p>\Large \underline {\underline {Question \: :}}$

In a triangle largest angle is 20° more than the smallest angle. 3rd angle is 10° more than the smallest angle. What is the sum of the angles in that triangle and what are the measures of the angles?

$\color {red} </p><p>\Large \underline {\underline {Answer \: :}}$

Sum of interior angle of a triangle = 180°

Let the smallest angle be x.

• Smallest angle = x
• Largest angle = 20° + x
• 3rd angle = 10° + x

So, our equation is :

x + 20 + x + 10 + x = 180

3x + 30 = 180

3x = 180 - 30

3x = 150

x = 150/3

x = 50

$\Longrightarrow$ So, measures of the angles :

• Smallest angle = x = 50°
• Largest angle = 20° + x = 20° + 50° = 70°
• 3rd angle = 10° + x = 10° + 50° = 60°

$\Longrightarrow$ Sum of the angles in the triangle :

50° + 70° + 60°

= 180°

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