Question

find the. value of y​

Answer 1

line m // line l and line t is their transversal

angle y + 135° = 180°.... interior angles

y = 180° – 135°

y= 45°

Answer 2

$\pink\bigstar$Answer:

$\boxed{\sf y\: =\:{45}^{\circ}}$

$\blue\bigstar$Given:

• m || l
• t is the transversal bisecting the lines m and l which are parallel.
• $\angle$CDF = 135°

$\red\bigstar$To find:

• The value of y.

$\pink\bigstar$ Solution:

$\because$ m || l and t is the transversal,

$\therefore$ $\angle$CDF + $\angle$DFG = 180°

( Interior angles on the same side of the transversal)

$\implies$ 135° + y = 180°

( Substitution of values)

$\implies$ y = 180° - 135°

$\implies$ $\boxed{\sf y \: = \: {45}^{\circ}\:}$

$\boxed{\sf \therefore y \: = \: {45}^{\circ}\:}$

$\blue\bigstar$ Concepts Used:

• Co - Interior angles Property (Sum of the Interior angles on the same side of the transversal is 180° )
• Substitution of given values
• Transposition Method

$\red\bigstar$Extra - Information:

• A transversal is a line that passes through two lines lying in the same plane at two distinct points.
• Corresponding angles formed by the intersection of transversal and a given pair of parallel lines, are equal.
• Alternate Interior angles and Alternate Exterior angles are equal, which are formed by the intersection of a transversal and a pair of given parallel lines.