Answer:
Explanation:
In a triangle, the sum of the three interior angles is always 180 degrees. Therefore, we can set up an equation based on this fact to find the measure of angle A.
Since AB is congruent to BC, angles A and C are congruent. Let's call their measure y:
y + y + (x+2+ x+23) = 180
Simplifying and combining like terms:
2y + 2x + 25 = 180
Subtracting 25 from both sides:
2y + 2x = 155
Dividing both sides by 2:
y + x = 77.5
Since we want to find the measure of angle A, which is x+23, we can substitute y = x+23 into the equation:
x+23 + x = 77.5
Simplifying and combining like terms:
2x + 23 = 77.5
Subtracting 23 from both sides:
2x = 54.5
Dividing both sides by 2:
x = 27.25
Therefore, the measure of angle A is:
x + 23 = 27.25 + 23 = 50.25 degrees