In a parallelogram ABCD, If ∠A = (3x + 12)°, ∠B = (2x - 32)° then find the value of x and then find the measures of ∠C and ∠D.

Concept: Types of Quadrilaterals > Properties of a Parallelogram

In the given figure, centre of two circles is O. Chord AB of bigger circle intersects the smaller circle in points P and Q. Show that AP = BQ.

Concept: Properties of Chord

In the given Figure, line AB || line CD and line PQ is the transversal. Ray PT and ray QT are bisectors of ∠BPQ and ∠PQD respectively. Prove that m∠PTQ = 90°.

Concept: Remote Interior Angles of a Triangle Theorem

In the given figure, line DE || line GF, ray EG and ray FG are bisectors of ∠DEF and ∠DFM respectively. Prove that,

(i) ∠DEG = `1/2∠"EDF"`

(ii) EF = FG.

Concept: Remote Interior Angles of a Triangle Theorem

In the following table, a ratio is given in each column. Find the remaining two ratios in the column and complete the table.

sin θ | `11/61` | `1/2` | `3/5` | ||||||

cos θ | `35/37` | `1/sqrt3` | |||||||

tan θ | `1` | `21/20` | `8/15` | `1/(2sqrt2)` |

Concept: Trigonometric Ratios and Its Reciprocal

**Write the following statement in conditional form.**

Concept: Concept of Plane

In which quadrant are the following points ?

Concept: Co-ordinates of Points on the Axes

As shown in the following figure, in ΔLMN and ΔPNM, LM = PN, LN = PM. Write the test which assures the congruence of the two triangles. Write their remaining congruent parts.

Concept: Congruence of Triangles

From the information given below, find which of the point is between the other two. If the points are not collinear, state so.

d(P, R) = 7, d(P, Q) = 10, d(Q, R) = 3

Concept: Co-ordinates of Points and Distance

From the information given below, find which of the point is between the other two.

If the points are not collinear, state so.

d(R, S) = 8, d(S, T) = 6, d(R, T) = 4

Concept: Co-ordinates of Points and Distance

From the information given below, find which of the point is between the other two.

If the points are not collinear, state so.

d(A, B) = 16, d(C, A) = 9, d(B, C) = 7

Concept: Co-ordinates of Points and Distance

If the points are not collinear, state so.

d(D, E) = 5, d(E, F) = 8, d(D, F) = 6

Concept: Co-ordinates of Points and Distance

If the points are not collinear, state so.

d(X, Y) = 15, d(Y, Z) = 7, d(X, Z) = 8

Concept: Co-ordinates of Points and Distance

If the points are not collinear, state so.

d(L, M) = 11, d(M, N) = 12, d(N, L) = 8

Concept: Co-ordinates of Points and Distance

Points X, Y, Z are collinear such that d(X,Y) = 17, d(Y,Z) = 8, find d(X,Z) .

Concept: Co-ordinates of Points and Distance

Concept: Co-ordinates of Points and Distance

Concept: Co-ordinates of Points and Distance

Concept: Co-ordinates of Points and Distance

**Select the correct alternative from the answer of the question given below.**

Concept: Co-ordinates of Points and Distance

**Select the correct alternative from the answer of the question given below.**

Concept: Co-ordinates of Points and Distance