The segment BK connects vertex B of triangle ABC with point K on the opposite side. Angles A and B of this triangle

| February 22, 2021 | education

The segment BK connects vertex B of triangle ABC with point K on the opposite side. Angles A and B of this triangle are respectively 65 degrees and 92 degrees. Find the angles of the triangle ABK and СBK, considering that the angle СKB is twice the angle BAC.

The angle of the BCA will be:

180 – (65 + 92) = 23 (°).

Let’s find the value of the ВKВ angle:

65 * 2 = 130 (°).

Then, in the ВKС triangle, the КBC angle is equal to the difference between 180 and two other angles:

180 – (130 + 23) = 27 (°).

Now you can find the angle ABC, if we know the angles ABC and KBC:

92 – 27 = 65 (°).

Or the angle ABK can also be found, knowing that in the triangle ABK the angle ВAK is 65 °, and the angle AKВ is adjacent to the ВKС angle and is equal to 180 – 130 = 50 °.

180 – (65 + 50) = 65 (°).

Answer: the angles of the triangle ABK and СBK are equal to 65 ° and 27 °, respectively.



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