Question

Given a pair of parallel lines that are cut by a transversal, if a pair of interior angles on the same side of the transversal measure 2x and 3x-5, find the two angles.​

Answer 1

Step-by-step explanation:

Given :-

A pair of parallel lines that are cut by a transversal, a pair of interior angles on the same side of the transversal measure 2x and 3x-5.

To find :-

Find the two angles ?

Solution :-

Given that

The measure of the pair of interior angles on the same side to the transversal = 2X° and (3X-5)°

We know that

If two parallel lines Intersected by a transversal then the pair of interior angles on the same side to the transversal are supplementary.

=> 2X° + (3X-5)° = 180°

=> 2X°+3X°-5° = 180°

=> 5X° -5° = 180°

=> 5X° = 180°+5°

=> 5X° = 185°

=> X° = 185°/5

=> X° = 37°

So,

2X° = 2×37° = 74°

and

(3X-5)° = 3(37°)-5° = 111°-5° = 106°

or 180°-74° = 106°

Therefore, required angles are 74° and 106°

Answer:-

The required angles for the given problem are 74° and 106°

Used formulae:-

• If two parallel lines Intersected by a transversal then the pair of interior angles on the same side to the transversal are supplementary.

Points to know:-

If two parallel lines Intersected by a transversal then

• The pair of exterior angles on the same side to the transversal are supplementary.

• The corresponding angles are equal.

• Vertically opposite angles are equal.

• Alternative interior angles are equal.

Answer 2

Given :-

A pair of parallel lines that are cut by a transversal, if a pair of interior angles on the same side of the transversal measure 2x and 3x-5.

To Find :-

The measures of the two angles.

Using Geometry Rules :-

Angles of the same side of the transversal are always be equal.

Process :-

Using the above rule,

$3x - 5 = 2x$

$3x - 2x = 5$

$x = 5$

Therefore we know the value x = 5. Substitute in the given angles.

$2x = 2(5) = 10$

$3x - 5 = 3(5) - 5 = 15 - 5 = 10$

Conclusion :-

The angles are 10 and 10.

Reason for being angles are equal :-

Angles of the same side of the transversal are always be equal.

HOPE IT HELPS