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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Solution

if two lines are parallel,
then sum of interior angles= $180^{\circ}$
So,
$\begin{matrix} 70^{\circ} + x = 180^{\circ} x = 110^{\circ} \end{matrix}$

Thus other angle is $110^{\circ}$

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Similar questions

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^°

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2 : 3, then the measure of the larger angle is

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 ___

If two parallel lines are intersected by a transversal, prove that the bisectors of the interior angles on the same side of transversal intersect each other at right angles.

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.

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Two parallel lines are intersected by a transversal .if the measure of one of the angles in a pair of interior angles is 70∘ . find the measure of the other

if two lines are parallel,then sum of interior angles=180∘So,70∘+x=180∘x=110∘Thus other angle is 110∘

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

if two lines are parallel,
then sum of interior angles= $180^{\circ}$
So,
$\begin{matrix} 70^{\circ} + x = 180^{\circ} x = 110^{\circ} \end{matrix}$

Thus other angle is $110^{\circ}$