The external angle at the vertex in the triangle ABC is equal to 103; the angle ACD is equal to 63

| August 12, 2021 | education

The external angle at the vertex in the triangle ABC is equal to 103; the angle ACD is equal to 63, find the value of the angle BAC.

We find the angle B of the triangle ABC, which in total with the outer angle is 180 °.
∠ ABC = 180 ° – ∠ B (external) = 180 ° – 103 ° = 77 °.
By the condition of the problem, the degree measure of one more angle ACB of the triangle ABC is known. Find the third angle BAC, knowing that the sum of the angles of the triangle is 180 °.
∠ BAC = 180 ° – (∠ ABC + ∠ ACB) = 180 ° – 140 ° = 40 °.
The problem can be solved if you know the external angle theorem, it is equal to the sum of two internal angles that are not adjacent to it. We get:
∠ BAC = ∠ В (external) – ∠ АСВ = 103 ° – 63 ° = 40 °.
Answer: the value of the angle BAC is 40 °.



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