contestada

in one triangle one of the angles is four times the measure of another and the third angle is five times as much as that angle what are the measurements of all three angles

Respuesta :

Answer:

The measurement of all three angles of Triangle are 18°  ,72°  ,90°

Step-by-step explanation:

Given as in a Triangle :

Let The angles of triangle are ∠A , ∠B , ∠C

From The property of Triangle.

The sum of measure of all the three angles of Triangle = 180°

So , ∠A + ∠B + ∠C =  180°

Now, According to question

∠A = 4 × ∠B

∠C = 5 × ∠B

∵ ∠A + ∠B + ∠C =  180°

Or, 4 × ∠B + ∠B + 5 × ∠B = 180°

Or, 10 × ∠B = 180°

∴   ∠B = [tex]\frac{180}{10}[/tex] = 18°

So,    ∠B = 18°

And  ∠A = 4 × 18° = 72°

        ∠C = 5 × 18° = 90°

Hence The measurement of all three angles of Triangle are 18°  ,72°  ,90° Answer