Advertisements
Advertisements
Question
Find the value of x in the given figure.
Solution
∠B = 180° – 120° .....(Sum of the opposite angles of a quadrilateral are supplementary)
∠B = 60°
∠BCA = 90° ...(Angle in a semicircle)
∠BAC + ∠B + ∠BCA = 180°
x + 60° + 90° = 180°
x + 150° = 180°
x = 180° – 150°
= 30°
The value of x = 30°
APPEARS IN
RELATED QUESTIONS
Prove that the “the opposite angles of the cyclic quadrilateral are supplementary”.
Prove that “The opposite angles of a cyclic quadrilateral are supplementary”.
Prove that, any rectangle is a cyclic quadrilateral
In the given figure, line PR touches the circle at point Q. Answer the following questions with the help of the figure.
(1) What is the sum of ∠ TAQ and ∠ TSQ ?
(2) Find the angles which are congruent to ∠ AQP.
(3) Which angles are congruent to ∠ QTS ?
(4) ∠TAS = 65°, find the measure of ∠TQS and arc TS.
(5) If ∠AQP = 42°and ∠SQR = 58° find measure of ∠ATS.
In the given figure, two circles intersect at points M and N. Secants drawn through M and N intersect the circles at points R, S and P, Q respectively. Prove that : seg SQ || seg RP.
In the given figure, two circles intersect each other at points A and E. Their common secant through E intersects the circles at points B and D. The tangents of the circles at points B and D intersect each other at point C. Prove that ▢ABCD is cyclic.
In the given figure, seg AD ⊥ side BC, seg BE ⊥ side AC, seg CF ⊥ side AB. Ponit O is the orthocentre. Prove that , point O is the incentre of ∆DEF.
MRPN is cyclic, ∠R = (5x – 13)°, ∠N = (4x + 4)°. Find measures of ∠R and ∠N, by completing the following activity.
Solution:
MRPN is cyclic
The opposite angles of a cyclic square are `square`
∠R + ∠N = `square`
∴ (5x – 13)° + (4x + 4)° = `square`
∴ 9x = 189°
∴ x = `square`
∴ ∠R = (5x – 13)° = `square`
∴ ∠N = (4x + 4)° = `square`
Prove the following theorems:
Opposite angles of a cyclic quadrilateral are supplementary.
In the figure, PQRS is cyclic, side PQ ≅ side RQ, ∠PSR = 110°. Find
(i) measure of ∠PQR
(ii) m(arc PQR)
(iii) m(arc QR)