Question

1. The measure of the largest angle of a triangle is 10 more than 3 times that of the smallest. It is also twice the measure of the second angle. What are the measures of the three angles of the triangle?

Answer 1

Answer for Question #44430 – Math - Algebra

1. The measure of the largest angle of a triangle is 10 more than 3 times that of the smallest. It is also twice the measure of the second angle. What are the measures of the three angles of the triangle?

Solution:

We will make the next notation:

- the largest angle = x

- the smallest angle = y

- the second angle = z

After description of the task we can build next system of equations:

$$\left\{ \begin{array}{c} x = 3y + 10{}^\circ \\ x = 2z \\ x + y + z = 180{}^\circ \end{array} \right.$$

(Sum of 3 angles of triangle always = 180)

From this:

$$\left\{ \begin{array}{c} y = \dfrac{x - 10{}^\circ}{3} \\ z = \dfrac{x}{2} \\ x + \dfrac{x - 10{}^\circ}{3} + \dfrac{x}{2} = 180{}^\circ \\ 6x + 2x - 20{}^\circ + 3x = 1080{}^\circ \\ 11x = 1100{}^\circ \\ x = 100{}^\circ \\ \left\{ \begin{array}{l} x = 100{}^\circ \\ y = 30{}^\circ \\ z = 50{}^\circ \end{array} \right. \end{array} \right.$$

Answer:

The angles of the triangle are:

- the largest angle = 100°

- the smallest angle = 30°

- the second angle = 50°

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