2. ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 150∘ . Then ∠BAC is equal to
Question
2. ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 150∘ . Then ∠BAC is equal to
Solution
In a cyclic quadrilateral, the sum of opposite angles is 180 degrees.
Given that ∠ADC = 150 degrees, and since AB is the diameter of the circle, ∠BAC is the angle subtended by the diameter at the circumference, which is always 90 degrees (a property of a circle).
However, since ∠ADC and ∠BAC are opposite angles in cyclic quadrilateral ABCD, their sum should be 180 degrees.
So, if ∠ADC = 150 degrees, then ∠BAC = 180 - 150 = 30 degrees.
Therefore, ∠BAC = 30 degrees.
Similar Questions
ABCD is a cyclic quadrilateral, ABX is a straight line and PQ is a tangent to the circle at A�Angle °CBX 85= , angle °BAQ 55= and angle °CAD 42=
ABCD is cyclic quadrilateral Sides AB and DC, when produced, meet at E, and sides BC and AD, When produced, meet at F. If ∠BFA=60° and ∠AED=30°, then the measure of ∠ABC is:Choices:- 85° 65° 75° 90°
is a triangle in which AB = AC . Let BC be produced to D . From a point E on the line AC let EF be a straight line such that EF is parallel to AB . Consider the quadrilateral ECDF thus formed. If ∠ABC = 65∘ and ∠EFD = 80∘ , then what is ∠FDC equal to?
ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120° and ∠BAC = 30°, the minimum possible value of ∠BCD is _____
ABCD is a parallelogram. If m∠DAB = 115 , then m∠BCD = _____?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.