Question

a transversal intersects two Parallel Lines if the measure of one of the angle is 40 degree then find the measure of its corresponding angle

Answer 1

Solution:

If a transversal intersects two Parallel Lines ,

if the measure of one of the angle is 40 degree

then to find the measure of its corresponding

angle

As we know that < ELB = < ALM [ vertically opposite angles]

< ELB = < ALM = 40°


< ELB = < LMD [ corresponding angles]


< ELB = < LMD = 40°


< LMD = < CMF [ vertically opposite angles]

< LMD = < CMF = 40°


< BLM + < LMD = 180°

<BLM = 140°

<BLM = 140° = <DMF [ corresponding angles]

<DMF = 140° = <CML [ vertically opposite angles]

<BLM = 140° = <ALE[ vertically opposite angles]

Thus one can calculate all the angles of transversal intersects two Parallel Lines,if one of the angle is given.

Answer 2

Given : measurement of one of the angles formed when two parallel lines intersect by a transversal is 40॰

To Find  : corresponding angle

Solution:

Properties of angles formed by transversal line  with two parallel lines :

• Corresponding angles are congruent.  

• Alternate angles are congruent.  ( Interiors & Exterior  both )  

• Interior angles are supplementary. ( adds up to 180°)

Corresponding angles are congruent

Hence measurement of corresponding angles are equal

measurement of one of the angle = 40°

Hence measurement of  corresponding angle is 40°

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