Question

the angles of a triangle are (x+10)°, (2x+5)° and (6x-15)° find x and the three angles​

Answer 1

Given :

• First angle is (x + 10)°
• Second angle is (2x + 5)°
• Third angle is (6x - 15)°
• Sum of all angles of a triangle is 180°

To find :

• Measure of three angles.

According to the question,

➜ (x + 10)° + (2x + 5)° + (6x - 15)° = 180°

➜ x + 10 + 2x + 5 + 6x - 15 = 180°

➜ 9x + 15 - 15 = 180°

➜ 9x + 0 = 180°

➜ 9x = 180°

➜ x = 180° ÷ 9

.°. x = 20°

• First angle is (x + 10)° = 20 + 10 = 30°
• Second angle is (2x + 5)° = 2 × 20 + 5 = 40 + 5 = 45°
• Third angle is (6x - 15)° = 6 × 20 - 15 = 120 - 15 = 105°

________________....

Verification :

Sum of all angles of a triangle should be 180°

➜ 30° + 40° + 105° = 180°

➜ 180° = 180°

.°. L.H.S = R.H.S

Hence,verified...

Answer 2

Answer:-

Given:-

Measurement of the int. angles of the triangle:-

1. (x + 10)°
2. (2x + 5)°
3. (6x - 15)°

To Find:-

Value of (x) and constant value of the angle measurements.

____________...

We know,

Sum of int. angles of a triangle = 180°

According to the Question:-

(x + 10)° + (2x + 5)° + (6x - 15)° = 180°

➵ x° + 10° + 2x° + 5° + 6x° - 15° = 180°

➵ 2x° + x° + 6x° + 10° + 5° - 15° = 180°

➵ 9x° + 15° - 15° = 180°

➵ 9x° = 180°

➵ x° = 180°/9

➵ x° = 20°

∴ First Angle = (x + 10)°

= (20 + 10)°

= 30°

Second Angle = (2x + 5)°

= (40 + 5)°

= 45°

Third Angle = (6x - 15)°

= (120 - 15)°

= 105°

Verification:-

LHS:-

(x + 10)° + (2x + 5)° + (6x - 15)°

= 30° + 45° + 105°

= 180°

RHS:-

180°

∴ LHS = RHS