Question

the angles of triangle are (x+10)°, (x+40)° and (2x+30)° find the measure of all angles​

Answer 1

Answer:

65⁰,35⁰,80⁰

Step-by-step explanation:

(x+40⁰)+(x+10)⁰+(2x+30)⁰=180⁰

4x⁰+80⁰=180⁰. (x+x+2x=4x). (40+10+30=80)

4x⁰=180⁰-80⁰

4x⁰=100⁰

x=100/4=25⁰

25+40=65⁰

25+10=35⁰

2(25)+30=50+30=80⁰

measure of all angles of a triangle is 180⁰ so we took 180⁰ there.

Answer 2

Given:

A triangle with

• 1st angle = (x + 10)°
• 2nd angle = (x + 40)°
• 3rd angle = (2x + 30)°

What To Find:

The measure of the angles of the triangle.

How to find:

To find the measure of all angle we have to know that sum of the interior angles of triangle is equal to 180° and substitute the value and solve.

Solution:

Using the property,

⇒ Sum of the interior angles of triangle = 180°

Put the values,

⇒ (x + 10)° + (x + 40)° + (2x + 30)° = = 180°

Remove the brackets,

⇒ x + 10 + x + 40 + 2x + 30 = 180

Rearrange the terms in LHS,

⇒ x + x + 2x + 10 + 40 + 30 = 180

Add the terms,

⇒ 4x + 80 = 180

Take 80 to to RHS,

⇒ 4x = 180 - 80

Subtract 80 from 180,

⇒ 4x = 100

Take 4 to RHS,

⇒ x = $\dfrac{100}{4}$

Divide 100 by 4,

⇒ x = 25°

Now substitute the values,

• 1st angle = (x + 10)° = (25 + 10)° = 35°
• 2nd angle = (x + 40)° = (25 + 40)° = 65°
• 3rd angle = (2x + 30)° = (2 × 25 + 30)° = (50 + 30)° = 80°

∴ Thus the angles of the triangles are 35°, 65° and 80° respectively.