Answer:
∠A = 52
∠B = 76
∠C = 52
Explanation:
We're given that triangle ABC is isosceles. That means that two of its sides and two of its angles will be the same. Therefore, angle ∠A will be equal to ∠C (we know this because they're formed by a line that goes through the two equal sides, both of which are marked by having lines through them).
Therefore, our three angles are:
∠A = (4x + 4)°
∠B = (5x + 16)°
∠C = (4x + 4)°
Per the properties of a triangle, we can also know that all the internal angles of a triangle should add up to 180°. So we can now set up an expression in which the three angles added together are equal to 180°
(4x + 4) + (5x + 16) + (4x + 4) = 180
Combining like terms --> 13x + 24 = 180
Subtract 24 from both sides --> 13x = 156
Divide both sides by 13 --> x = 12
Now that we've found that x=12, we can just substitute 12 for x to get each angle:
∠A = 4x + 4 = 4(12) + 4 = 52
∠B = 5x + 16 = 5(12) + 16 = 76
∠C = 4x + 4 = 4(12) + 4 = 52
Hope this helps! :)