Final answer:
Each base angle in the isosceles triangle, where the vertex angle measures 46 degrees, would be 67 degrees since the sum of angles in a triangle equals 180 degrees.
Step-by-step explanation:
The student has asked what the measure of the basic angle of an isosceles triangle would be if the vertex angle measures 46 degrees, and the two congruent sides measure 21 inches. To determine the measure of a basic angle in an isosceles triangle, we can use the fact that the sum of all angles in a triangle must equal 180 degrees. In an isosceles triangle, the two base angles are congruent, meaning they have the same measure.
So, we can represent the measure of each base angle as 'x'. With this, we would set up the equation: 2x + 46 = 180, as there is the vertex angle and two base angles that add up to 180 degrees. Solving this equation for 'x' gives us:
- 2x = 180 - 46
- 2x = 134
- x = 134 / 2
- x = 67 degrees
Therefore, the measure of each of the base angles in the isosceles triangle is 67 degrees.