Answer:
Using the information from the problem, the measurement of ∠A is 55°
Step-by-step explanation:
We are given that ΔABC is isosceles. If a triangle is isosceles, then it means that two angles are going to be congruent to each other which are called the base angles. In the problem above, ∠A and ∠C are the base angles so that means that their measurements are going to be equal to each other.
We can use this information in order to solve the problem and find the measurement of ∠A. By doing so, we will set up both expressions and equal them to each other.
m∠A = 3x + 40
m∠C = x + 50
3x + 40 = x + 50
Subtract x on both sides of the equation.
2x + 40 = 50
Subtract 40 from both sides of the equation.
2x = 10
Divide 2 on both sides of the equation.
x = 5
So now that we have our x-value, we will plug this into both angles just to check our work. If they have the same measurement, then we have our answer for the measurement of ∠A.
x = 5
m∠A = 3(5) + 40
m∠A = 15 + 40
m∠A = 55
m∠C = (5) + 50
m∠C = 55
So, the two angles have the same measurements to each other which means they are congruent. Now, we have our answer.
The measurement of ∠A is 55°
