English, asked by amlansatpathy, 5 months ago

If the semicircle drawn with one side of a triangle as diameter passes through the opposite vertex, then the measure of the angle at the vertex is_______ degree

Answers

Answered by Rameshjangid

Answer:90 Degrees, for a half circle, the intercepted arc measures 180°, so each corresponding inscribed angle is half that.

Explanation:

∆OBA and ∆OBC are isosceles triangles, and by the equality of the base angles of an isosceles triangle, ∠OBC = ∠OCB and ∠OBA = ∠OAB.

Let α = ∠BAO and β = ∠OBC. The three internal angles of the ∆ABC triangle are α, (α + β), and β. Since the sum of the angles of a triangle is equal to 180°, we have

α + (α + β) + β = 180°

2α + 2β = 180°

2(α + β) = 180°

α + β = 90°

Hence, Angle ABC = 90°

If the semicircle drawn with one side of a triangle as diameter passes through the opposite vertex, then the measure of the angle at the vertex is_______ degree​

Answers

If the semicircle drawn with one side of a triangle as diameter passes through the opposite vertex, then the measure of the angle at the vertex is_______ degree