Answer/Step-by-step explanation:
a. First, find the value of a.
Sum of the interior angles of a triangle = 180° (triangle sum theorem)
Therefore:
3a + 2a + a = 180°
Add like terms
6a = 180°
6a/6 = 180/6
a = 30
Thus:
a = 30°
2a = 2(30) = 60°
3a = 3(30) = 90°
b. The triangle is an isosceles triangle because it has two sides that are indicated to be equal. This also implies that the angels opposite each of the equal sides are also congruent to each other.
Therefore, sum of the isosceles triangle would be:
2(2x) + 5x = 180°
4x + 5x = 180
9x = 180
9x/9 = 180/9
x = 20
Thus:
2x = 2(20) = 40
5x = 5(20) = 100