Question

Two parallel lines, l and m are cut by a transversal t. If the interior angles of the same side of t be (2x-8)° and (3x-7)°, find the measure of each of these angles

Answer 1

━━━━━━━━━━━━━━━━━━━━

⏏ Required Answer:

✏ GiveN:

• Two parallel lines m and n are cut by tranversal t
• Interior angles on same side are (2x - 8)° and (3x - 7)°

✏ To FinD:

• Find measure of the angles.

━━━━━━━━━━━━━━━━━━━━

⏏ How to solve?

❇ We need to know a theoram related to this:

$\large{ \bold{ \underline{ \underline{ \red{Theoram \leadsto}}}}}$

If two parallel lines are cut by any other line, i.e. transversal, then each pair of consecutive interior angles are supplementary. They add upto 180°.

✏Now, we can solve the question because we have the measure of the two angles and also they add upto 180°

━━━━━━━━━━━━━━━━━━━━

⏏ Solution:

• Consecutive interior angles add upto 180°

Given,

• Measure of interior angles are (2x - 8)° and (3x - 7)°

According to theoram,

➙ 2x - 8 + 3x - 7 = 180°

➙ 5x - 15 = 180°

➙ 5x = 195°

➙ x = 195°/5

➙ x = 39°

Then, our Required angles are,

➙ 2x - 8 = 2(39) - 8 = 70°

➙ 3x - 7 = 3(39) - 7 = 110°

$\large{ \therefore{ \underline{ \underline{ \pink{ \rm{Hence \: solved \: \dag}}}}}}$

━━━━━━━━━━━━━━━━━━━━

Answer 2

interior angle 1 = (2x-8)°

interior angle 2 = (3x-7)°

sum of interior angles = 180°

interior angle 1 + interior angle 2 = 180°

(2x-8)° + (3x-7)° = 180°

2x + 3x - 8 - 7 = 180°

5x - 15 = 180°

5x = 195°

x = 195/5 = 39

interior angle 1 = (2x-8)° = 70°

interior angle 2 = (3x-7)° = 110°