In order to find the values of the angles A and C in an isosceles ΔABC with the base of the AC, given that the angle B is 40 °, you first need to remember the rule.
According to this rule, in an isosceles triangle, the angles at the base are equal.
In the considered ΔABC, the base is AC.
This means that the angles to be determined, as well as the angles at the base AC, are angles A and C.
Now let’s write for angles A and C.
A = C.
A + B + C = 180 °.
2A + B = 180 °.
2A = 180 ° – B.
2A = 180 ° – 40 °.
2A = 140 °.
A = 140 °: 2.
A = 70 °.
A = C = 70 °.
Answer: 70 °, 70 °.
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