Question

(a) problem 10: find the measures of the angles of a triangle whose angles have measures in the ratio of 1:5:6. also, what kind of triangle is it?

Explanation:

Step1: Let the angles be x, 5x, 6x

Since the sum of angles in a triangle is 180°.

Step2: Set up the equation

$x + 5x+6x=180$

Step3: Combine like terms

$12x = 180$

Step4: Solve for x

$x=\frac{180}{12}=15$

Step5: Find the angles

First angle: $x = 15°$
Second angle: $5x=5\times15 = 75°$
Third angle: $6x=6\times15 = 90°$
Since one angle is 90°, it is a right - triangle.

Answer:

The angles are 15°, 75°, 90°. It is a right - triangle.