Final answer:
Using the properties of an isosceles triangle and the sum of angles in a triangle, the angle at point B is calculated to be 84°. Setting this equal to the given expression for m∠B results in the solution for x being 20, which does not match any of the provided options. It's important to double-check the given values and the solution if there is a discrepancy.
Step-by-step explanation:
To determine the value of x in triangle ABC where angles A and B are given, and triangle ABC is isosceles, we use the properties of an isosceles triangle. The angles at the base of an isosceles triangle are equal, so if m∠A is 48°, then m∠C is also 48° because they are at the base of the triangle. Since the sum of angles in any triangle is 180°, we can find m∠B as follows:
m∠B = 180° - m∠A - m∠C
m∠B = 180° - 48° - 48°
m∠B = 84°
The question states m∠B = 4x + 4. To find x, we set up the equation:
4x + 4 = 84°
Subtract 4 from both sides:
4x = 80°
Divide both sides by 4 to solve for x:
x = 20°
However, none of the given options matches our solution. It's possible there is a typo or a mistake in the given values or the options. Assuming that, the most appropriate course of action would be to double-check the values provided and the solution.