Question

In triangle ABC angle A is equal to 3x +16 Angle B is equals to X +7 and angle C is equal to 5x - 14

Answer 1

Answer:

x=19

Step-by-step explanation:

Angle A +angle B +angle C=180°(Angle sum property of triangle

3x+16+X+7+5x-14=180°

9x+9=180°

9x=171

x=19

Answer 2

Answer:

NOTE: Sum of all the three interior angles of a triangle is equal to 180°.

If we consider a triangle, say ∆ABC ,

Then,

angle A + angle B + angle C = 180°

Here, it is given that,

angle A = 3x + 16°

angle B = x + 7°

angle C = 5x - 14°

Now,

According to the property of triangle,

We have,

=> angle A + angle B + angle C = 180°

=> (3x+16°)+(x+7°)+(5x-14°)=180°

=> 9x + 9° = 180°

=> 9(x+1°) = 180°

=> x + 1° = 180°/9

=> x + 1° = 20°

=> x = 20° - 1°

=> x = 19°

Thus, the angles of given triangle are;

angle A = 3x + 16°

= 3•19° + 16°

= 57° + 16°

= 73°

angle B = x + 7°

= 19° + 7°

= 26°

angle C = 5x - 14°

= 5•19° - 14°

= 95° - 14°

= 81°

Thus, the angles of the given triangle are; 73° , 26° , 81°

Verification;

According to the property of the triangle,

the sum of the interior angles is equal to 180°.

Here, the obtained angles are ;

73° , 26° and 81°.

Let's sum up all the three angles,

Then we get ,

Sum of angles = 73° + 26° + 81°

= 180°

Here, the obtained sum is 180°,

Hence, the angles thus obtained are right.