Question

Question 2 help please

Answer 1

Answer:

The measure of the vertex angle is 94 degrees ⇒ A

Step-by-step explanation:

• In any triangle, the sum of the measures of its interior angle is 180°

• In the isosceles triangle, the two base angles are equal in measures

∵ In an isosceles triangle, the measure of the base angle = (2x + 5)

∵ The base angles of the isosceles triangles are equal in measures

∴ The measures of the base angles are (2x + 5), (2x + 5)

∵ The measure of the vertex angle = (5x - 1)

∵ The sum of the measure of the three angles = 180°

∴ (2x + 5) + (2x + 5) + (5x - 1) = 180

→ Add the like terms in the left side

∵ (2x + 2x + 5x) + (5 + 5 + -1) = 180

∴ 9x + 9 = 180

→ Subtract 9 from both sides

∴ 9x + 9 - 9 = 180 - 9

∴ 9x = 171

→ Divide both sides by 9 to find x

∴ x = 19

→ Substitute the value of x in the measure of the vertex angle to find it

∵ The measure of the vertex angle = 5x - 1

∴ The measure of the vertex angle = 5(19) - 1

∴ The measure of the vertex angle = 95 - 1

∴ The measure of the vertex angle = 94°

∴ The measure of the vertex angle is 94 degrees