Question

(a) problem 12: find the measures of the angles of a triangle whose angles have measures x, x + 10, and x + 20. also, tell what kind of triangle this is with respect to its angles.

Explanation:

Step1: Apply angle - sum property

The sum of angles in a triangle is 180°. So, $x+(x + 10)+(x + 20)=180$.

Step2: Simplify the equation

Combining like terms, we get $3x+30 = 180$.

Step3: Solve for x

Subtract 30 from both sides: $3x=180 - 30=150$. Then divide by 3, $x = 50$.

Step4: Find angle measures

Substitute $x = 50$ into the angle expressions. The angles are $x=50^{\circ}$, $x + 10=60^{\circ}$, $x + 20=70^{\circ}$.

Step5: Classify the triangle

Since all angles ($50^{\circ},60^{\circ},70^{\circ}$) are less than 90°, it is an acute - angled triangle.

Answer:

The angle measures are 50°, 60°, 70°. It is an acute - angled triangle.