Answer:
In an isosceles triangle, the base angles (angles opposite the congruent sides) are equal in measure. In this case, angles B and C are the base angles, and their measurements are given as (7x - 27)° and (5x - 5)°, respectively. Since angles B and C are equal, we can set up an equation: (7x - 27)° = (5x - 5)° To solve for x, we can simplify the equation: 7x - 27 = 5x - 5 Subtracting 5x from both sides: 2x - 27 = -5 Adding 27 to both sides: 2x = 22 Dividing both sides by 2: x = 11 Now that we have found the value of x, we can substitute it back into one of the base angles to find the measure of angle A. m∠A = 180° - m∠B - m∠C m∠A = 180° - (7x - 27)° - (5x - 5)° Substituting x = 11: m∠A = 180° - (7 * 11 - 27)° - (5 * 11 - 5)° Simplifying further: m∠A = 180° - (77 - 27)° - (55 - 5)° m∠A = 180° - 50° - 50° m∠A = 80° Therefore, the measure of angle A in triangle ABC is 80°. If you have any further questions or need clarification, feel free to ask
Explanation: