If y=15, then what is \angle ACB equal to?
Consider the following for the next two (02) items that follow:<br>In the following figure, a triangle ABC is inscribed in a circle with centre at O. Let \angle POA=x^{\circ} and \angle OQB=y^{\circ}. Further, OB = BQ.
- A. 30^{\circ}
- B. 40^{\circ}
- C. 45^{\circ}
- D. 60^{\circ} ✓
Correct Answer: D. 60^{\circ}
Explanation
For y=15, the central angle \angle AOB = 180^{\circ} - (\angle OAB + \angle OBA) = 180^{\circ} - 4y = 120^{\circ}. The inscribed angle \angle ACB subtending the same arc is half of the central angle, so \angle ACB = \frac{120^{\circ}}{2} = 60^{\circ}.
Related questions on Geometry
- In a triangle ABC, \angle A = 30^\circ, AB = 7 cm and AC = 12 cm. What is the area of the triangle ABC?
- ABC is a triangle right angled at B. D is a point on AC such that BD is perpendicular to AC. If AB = p and BC = \sqrt{3}p, then what is BD...
- The difference between an interior angle and an exterior angle of a regular polygon is 120°. What is the number of sides of the polygon?
- An angle q is exactly one-fourth of its complementary angle. What is the value of angle q?
- The sides of a triangle are 11 cm, 60 cm and 61 cm. What is the area of the triangle formed by joining the mid-points of the sides of the tr...