Question

Find the value of x. if l || m

Answer 1

Answer:

x= 45

Step-by-step explanation:

Since l || m,

corresponding angles = 135

135 + x = 180 (straight line)

x = 180 - 135

x = 45

Answer 2

$\Large{\underline{\bf{Solution:-}}}$

Here we go!

So here we see that the two lines are parallel to each other so which means we may have a lot of combinations as follows,

☆ Internal opposite angles are equal

☆ External opposite angles are equal

☆ Adjacent angles add up to 180°

☆ Co-interior angles add up to 180°

☆ Vertically Opposite Angles are equal.

[From these rules we may derive the needed values]

∠ ABP = ∠ TCX

∠ ABP = 135° { By Vertically Opposite Angle }

∠ TCX = 135°

Now,

∠ TCX and ∠ ABQ together making supplementary angle.

So,

The sum of ∠ TCX and ∠ ABQ will be equal to 180°

∠ TCX + ∠ ABQ = 180°

135° + ∠ ABQ = 180°

∠ ABQ = 180° - 135°

∠ ABQ = 45°

$\large{\boxed{\bold{x \:=\: 45^{\circ} }}}$

★ What is Parallel lines?

➹ Two different lines in a plane are said to be parallel, if there is no point common in them even through these lines are extended on both sides to any extent.

You have to know , all this relation which formed when two lines are parallel and a transversal line intersecting it at some point.

★ What is Vertically Opposite Angle?

➹ Two angles are called a pair of vertically opposite angles, if their arms form two pairs of opposite rays.

★ What is Corresponding angles?

➹ The angles which occupy the same relative position at each intersection where a straight line crosses two others are known as corresponding angles. If the two lines are parallel, the corresponding angles are equal.

★ What is Linear pair of angles?

➹ Two adjacent angles of which different arms are opposite rays are called linear pair of angles.

★ What is Supplementary angles?

➹ If the sum of two angles is 180°, these are called supplementary angles.

For example, two angles measuring 62° and 118° are supplementary angles, because 62° + 118° = 180°.

★ What is Complementary angles?

➹ Two angles, the sum whose measure is 90°, are called complementary angles.

For example, angles measuring 30° and 60° are complementary angles as their sum is equal to 90° (30°+ 60° = 90°).

I m attaching one figure to understand the relation between angles more appropriately.

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