Question

In an isosceles triangle, the measure of a base angle is (2x + 5). At the vertex, the measure of an exterior angle is (5x - 3). Find the measures of the angles of the triangle.

a) Base angle: 2x + 5, Exterior angle: 5x - 3, Third angle: 2x + 5
b) Base angle: 2x + 5, Exterior angle: 5x - 3, Third angle: 90 degrees
c) Base angle: 90 degrees, Exterior angle: 2x + 5, Third angle: 5x - 3
d) Base angle: 5x - 3, Exterior angle: 2x + 5, Third angle: 2x + 5

Answer 1

In an isosceles triangle, the measures of the base angles are congruent. To find the measures of the angles in the triangle, we can set up an equation and solve for x. After finding the value of x, we can substitute it back into the expressions for the angles to get their measures.

Step-by-step explanation:

In an isosceles triangle, the measures of the base angles are congruent. So, if one base angle has a measure of (2x + 5), the other base angle also has a measure of (2x + 5).

In a triangle, the sum of the angles is 180 degrees. So, we can set up an equation:

(2x + 5) + (2x + 5) + (5x - 3) = 180

Simplifying the equation, we get:

4x + 7x + 2 = 180

11x + 2 = 180

11x = 178

x ≈ 16.18

Now we can substitute this value of x back into the expressions for the angles to find their measures:

Base angle = 2x + 5 ≈ 2(16.18) + 5 ≈ 37.36 degrees

Exterior angle = 5x - 3 ≈ 5(16.18) - 3 ≈ 78.9 degrees

Third angle = base angle = 37.36 degrees