Question

The vertex angle of an isosceles triangle measures 42°. A base angle in the triangle has a measure given by (2x + 3)°. What is the value of x? What is the measure of each base angle?

Answer 1

Answer:

• x = 33
• base angles: 69°

Step-by-step explanation:

The sum of angles in a triangle is 180°. In an isosceles triangle, the base angles are congruent.

For this, it is easiest to find the base angles first. If we let b represent the measure of one of them, the sum of angles is ...

  2b +42 = 180

  b +21 = 90 . . . . . . divide by 2

  b = 69 . . . . . . . subtract 21

The measure of the base angles is 69°.

__

Then we can find the value of x from its relation to the base angle measure:

  (2x +3)° = 69°

  2x = 66 . . . . . . . . . divide by °, subtract 3

  x = 33 . . . . . . . . divide by 2

The value of x is 33.