Question

If three angles of a triangle are (3x – 17 ), ( x + 40 ) and ( 2x – 5 ). Then

Find the value of x.​

Answer 1

Given

We have given three angles of a triangle which is (3x-17)° , (x+40)° & (2x-5)°

To find

We have to find the value of x

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Concept:

Since,we know that the sum of all angles in a triangle makes 180°.

How to solve:

step 1:First we add all the given angles and makes equal to 180° according to the angle sum property of triangle.

Step 2: Evaluate and solve the Equation and hence we will find the value of x.

Let the first angle be ∠A

Second angle be ∠B

And third angle be ∠C

Now, applying angle sum property:

∠A+∠B+∠C=180°

=>(3x-17)+(x+40)+(2x-5)=180

=>3x-17+x+40+2x-5=180

=>3x+x+2x-17+40-5=180

=>6x+18=180

=>6x=180-18

=>6x=162

=>x=162÷6

=>x=27

Hence,the first angle be 3x-17= 81-17=64°

Second angle be x+40= 27+40=67°

Third angle be 2x-5= 54-5=49°

Check:

∠A+∠B+∠C=180°

=>64°+67°+49°=180°