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scoundrel [369]
3 years ago
15

An isosceles triangle △ABC with the base BC is inscribed in a circle. Find the measures of angles of the triangle, if measure of

arc BC is 102°.
Mathematics
1 answer:
____ [38]3 years ago
6 0

Answer:

  • angle at A: 51°
  • base angles: 64.5°

Step-by-step explanation:

The measure of the inscribed angle BAC is half the measure of the intercepted arc BC, so is 102°/2 = 51°.

The base angles  at B and C are the complement of half this value, or ...

  90° -(51°/2) = 64.5°

The angle measures in the triangle are ...

  ∠A = 51°

  ∠B = ∠C = 64.5°

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