Advertisements
Advertisements
Question
In a cyclic ▢ABCD, twice the measure of ∠A is thrice the measure of ∠C. Find the measure of ∠C?
Options
36°
72°
90°
108°
Advertisements
Solution
72º
Explanation:
ABCD is a cyclic quadrilateral.
2∠A = 3∠C ...(1) (Given)
Now, ∠A + ∠C = 180º ...(Opposite angles of a cyclic quadrilateral are supplementary)
⇒ `3/2 ∠C + ∠C = 180^circ` ...[From (1)]
⇒ `(3/2 + 1) ∠C = 180^circ`
⇒ `5/2 ∠C = 180^circ`
⇒ `∠C = (2 xx 180^circ)/5`
⇒ ∠C = 72º
Thus, the measure of ∠C is 72º.
RELATED QUESTIONS
In the given figure, ∆QRS is an equilateral triangle. Prove that,
- arc RS ≅ arc QS ≅ arc QR
- m(arc QRS) = 240°.
In the given figure, chord AB ≅ chord CD, Prove that, arc AC ≅ arc BD.
In the given figure, in a circle with centre O, length of chord AB is equal to the radius of the circle. Find measure of each of the following.
(1) ∠ AOB (2)∠ ACB
(3) arc AB (4) arc ACB.
Points A, B, C are on a circle, such that m(arc AB) = m(arc BC) = 120°. No point, except point B, is common to the arcs. Which is the type of ∆ABC?
`square`PQRS is a parallelogram. Write the sum of measures of ∠P and ∠ Q.
From the information given in the figure, find the measure of ∠ AEC.
In the given figure, two circles intersect each other at points S and R. Their common tangent PQ touches the circle at points P, Q.
Prove that, ∠ PRQ + ∠ PSQ = 180°
In the figure given above, O is the centre of the circle. Using given information complete the following table:
| Type of arc | Name of the arc | Measure of the arc |
| Minor arc | `square` | `square` |
| Major arc | `square` | `square` |
What is the measure of a semicircular arc?
In figure, in a circle with center O, length of chord AB is equal to the radius of the circle. Find measure of each of the following.
- ∠AOB
- ∠ACB
- arc AB
In the figure, quadrilateral ABCD is cyclic. If m(arc BC) = 90° and ∠DBC = 55°, then find the measure of ∠BCD.
Chord AB and chord CD of a circle with centre 0 are congruent. If m(arc AB) = 120°, then find the m(arc CD).
