Question

(2x)°(3x+5)°(4x-14)°are angles of a triangle find each angles​

Answer 1

Required Answer :-⤵️

1st Angle of triangle = 21°

2nd Angle of triangle = 68°

3rd Angle of triangle = 70°

Given :

. First Angle = 2x°

. second Angle = (3x+5)°

. Third Angle = ( 4x -14)°

To find :

. Measure of each Angle of triangle.

Explanation :

According to the given question,

(2x)°, (3x+5)°, (4x-14)° are the angles of triangle.

So,

We know that sum of interior angles of triangle is always 180°.

Hence, we can say that,

(2x)°+ (3x+5)°+(4x-14)° = 180°

=> (9x - 9) ° = 180°

=> 9x = 180° + 9°

=> 9x = 189°

=> x = 189/9

=> x = 21°

Now, We have the value of x = 21°

Let's put it into the unknown Angle of triangle.

. First

=> 2x°

=> 2× 21°

=> 42°

So, first Angle of this triangle = 42°

. Second

=> (3x + 5)°

=> ( 3×21+ 5)

=> (63 + 5 )°

=> 68°

So, second Angle of this triangle = 68°

. Third

=> ( 4x - 14)°

=> ( 4×21 -14)

=> (84 -14)°

=> 70°

So, third angle of triangle = 180°

Verification :

To verify our statement, we have add three sides of triangle and equate it with 180° and make LHS = RHS.

let's do it ....

sum of three angles of triangle = 180°

=> 42° + 68° + 70° = 180°

=> 110° + 70° = 180°

=> 180° = 180°

LHS = RHS

hence, here we found LHS = RHS

so,

it is Verified.

Answer 2

Answer:

• ∠A = 42°
• ∠B = 68°
• ∠C = 70°

Explanation:

Given

• ∠A = (2x)°
• ∠B = (3x + 5)°
• ∠C = (4x - 14)°

To find

• Measure of each angle in the triangle

Solution

∠A + ∠B + ∠C = 180° (Angle sum property)

• (2x)° + (3x + 5)° + (4x - 14)° = 180°
• 2x + 3x + 5 + 4x - 14 = 180°
• 9x - 9 = 180°
• 8x = 189
• x = 189/9
• x = 21°

Hence, the angles are:

• ∠A = (2x)° = 2(21) = 42°
• ∠B = (3x + 5)° = 63° + 5° = 68°
• ∠C = (4x - 14)° = 84° - 14° = 70°

Verification

• ∠A + ∠B + ∠C = 180°
• 42° + 68° + 70° = 180°
• 110° + 70° = 180°
• 180° = 180°
• L.H.S = R.H.S