Select the correct alternative and fill in the blanks in the following statements.

(i) If a transversal intersects two parallel lines then the sum of interior angles on the same side of the transversal is ............

(A) 0^° (B) 90^°(C) 180^° (D) 360^°

(ii) The number of angles formed by a transversal of two lines is ............

(A) 2 (B) 4 (C) 8 (D) 16

(iii) A transversal intersects two parallel lines. If the measure of one of the angles is 40^∘ then the measure of its corresponding angle is .............

(A) 40^°(B) 140^° (C) 50^° (D) 180^°

(iv) In $∆$ ABC, $∠$ A = 76^° , $∠$ B = 48^°, $∴$ C = ..............

(A) 66 ° (B) 56 ° (C) 124 ° (D) 28 °

(v) Two parallel lines are intersected by a transversal. If measure of one of the alternate interior angles is 75^° then the measure of the other angle is .............

(A) 105^° (B) 15^° (C) 75^° (D) 45^°

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Solution

(i) It is known that, when two parallel lines are intersected by a transversal, then pairs of interior angles on the same side of transversal are supplementary i.e., sum of the interior angles on the same side of transversal is 180^∘.
Hence, the correct answer is option (C).

(ii)

In the above figure, line n is a transversal of line l and line m. The angles formed by the transversal n of two lines l and m are :
a, b, c, d, e , f , g and h.
∴ the number of angles formed by a transversal of two lines is 8.
Hence, the correct answer is option (C).

(iii)

Suppose line RP || line MS and line DK is the transversal intersecting them at H and G respectively.
Let ∠DHP = 40^∘
Now, ∠HGS is the corresponding angle of ∠DHP.
It is known that, corresponding angles formed by a transversal of two parallel lines are of equal measure.
∴ ∠HGS = 40^∘
Hence, the correct answer is option (A).

(iv) In ∆ABC,
∠A + ∠B + ∠C = 180^∘ (Angle sum property of triangle)
⇒76^∘ + 48^∘ + ∠C = 180^∘
⇒124^∘ + ∠C = 180^∘
⇒∠C = 180^∘ − 124^∘ = 56^∘
Hence, the correct answer is option (B).

(v)

Suppose line RP || line MS and line DK is the transversal intersecting them at H and G respectively.
Let ∠PHG = 75^∘
Now, ∠MGH is the alternate angle to ∠PHG.
It is known that, alternate interior angles formed by a transversal of two parallel lines are of equal measure.
∴ ∠MGH = 75^∘
Hence, the correct answer is option (C).

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Similar questions

Fill in the blanks in each of the following to make the statement true:
(i) If two parallel lines are intersected by a transversal then each pair of corresponding angles are ___
(ii) If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are ___
(iii) Two lines perpendicular to the same line are ___ to each other.
(iv) Two lines parallel to the same line are to ___ each other.

(v) If a transversal intersects a pair of lines in such a way that a pair of alternate angles are equal, then the lines are ___
(vi) If a transversal intersects a pair of lines in such a way that the sum of interior angles on the same side of transversal is $180^{0}$ , then the lines are ___

Which of the following statements are true (I) and which are false (F)? Give reasons.
(i) If two lines are intersected by a transversal, then corresponding angles are equal.
(ii) If two parallel lines are intersected by a transversal, then alternate interior angles are equal.
(iii) Two lines perpendicular to the same line are perpendicular to each other.
(iv) Two lines parallel to the same line are parallel to each other.
(v) If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.

Q. (i) If a transversal intersects two parallel lines then state the relation between alternate angles.
(ii) If each of the two parallel lines are parallel to the third line then what is the relation between them?
(iii) If a transversal intersects two parallel lines and the corresponding sides of two angles are parallel then what is the relation between these angles?
(iv) If AB is a line and P is a point outside it then how many lines can be drawn through P and Parallel to AB?
(v) If a transversal intersects two parallel lines such that the ratio between the interior angles on one of its side is 2:7, then find the measure of the greater angle.

Q. A transversal intersects two parallel lines. if the measure of one of the angle is

50^{0}

, then the measure of its corresponding angle is ................

Q. Two parallel lines are intersected by a transversal .if the measure of one of the angles in a pair of interior angles is

70^{\circ}

. find the measure of the other

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