Points M and N are taken on the circle on opposite sides of the diameter AB. It is known that ∠NBA = 68 °.
| September 7, 2021 | education
Points M and N are taken on the circle on opposite sides of the diameter AB. It is known that ∠NBA = 68 °. Find the corner NMB.
Consider a triangle ABN.
Since AB is the diameter, triangle ABN is right-angled with right angle ANB.
According to the problem statement, the angle ∠NBA = 68 °.
Then ∠NAB = 180 ° – ∠ANB – ∠NBA = 180 ° – 90 ° – 68 ° = 22 °.
Note that the angles ∠NAB and ∠NMB rest on the same arc NB,
therefore they are equal.
Therefore, ∠NMB = 22 °.
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