The angle of inscribed polygon m∠MNT from the triangle ABC is 45°
What is an inscribed polygon?
An inscribed polygon is a polygon whose vertices lie on the circle and the circle inscribing the polygon is known to be a circumscribed circle. But let's not forget that the circle is also inscribed in another right-angle triangle.
However, using the inscribed right angle theorem:
Supposed that a right triangle is inscribed in a circle;
- We can infer that the hypotenuse is the diameter of the circle.
From the given image, line MN is the diameter of the circle since that is the only diameter in the circle.
- And the angle facing the diameter is the right angle. i.e ∠T = 90°
We know that the sum of angles in a triangle is 180°. So, if ∠T = 90°, ∠N and ∠M = x
i.e.
90° + x + x = 180°
90° + 2x = 180°
2x = 180° - 90°
2x = 90°
x = 90°
x = 45°
Therefore, we can conclude that angle m∠MNT = 45°
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