Answer:
The measure of a base angle of one of the triangles is 54°
Step-by-step explanation:
<em>In the isosceles triangle, the angle between the two equal sides called the </em><em>vertex angle</em><em> and the other two angles are </em><em>equal </em><em>and called </em><em>base angles</em>
∵ The total number of degrees in the center is 360°
∵ All five vertex angles meeting at the center are congruent
→ To find the measure of each vertex divide 360° by 5
∴ The measure of each vertex = 360° ÷ 5
∴ The measure of each vertex = 72°
∵ The base angles are equal in the isosceles triangle
∵ The sum of the measures of the angles of a triangle is 180°
→ Assume that the measure of each base angle is x
∴ x + x + 72° = 180°
∴ 2x + 72° = 180°
→ Subtract 72 from both sides
∵ 2x + 72 - 72 = 180 - 72
∴ 2x = 108
→ Divide both sides by 2 to find x
∴ x = 54
∴ The measure of each base angle = 54°
∴ The measure of a base angle of one of the triangles is 54°
