Question

if angle 1 is 45 then find measurement of other angles 2,3,6,7,8​

Answer 1

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: Question :- \: \star}}}}}$

If angle 1 is 45° then find measurement of other angles 2,3,6,7,8.

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

∠2 = 135°

∠3 = 45°

∠6 = 135°

∠7 = 135°

∠8 = 45°

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

❁ ∠1 = 45°

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

◈ The value of,

∠2

∠3

∠6

∠7

∠8

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

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]

Finding ∠2

➝ ∠1 + ∠2 = 180°

[Adjacent angles]

➝ 45° + ∠2 = 180°

➝ ∠2 = 180° - 45

$\large{\boxed{\bold{∠2\:=\:135°}}}$

Finding ∠3

➝ ∠1 = ∠3

[Vertically Opposite]

➝ ∠3 = 45°

$\large{\boxed{\bold{∠3\:=\:45°}}}$

Finding ∠6

➝ ∠3 + ∠6 = 180°

[Co-interior angle]

➝ 45° + ∠6 = 180°

➝ ∠6 = 180°- 45°

$\large{\boxed{\bold{∠6\:=\:135°}}}$

Finding ∠7

➝ ∠6 = ∠7

[Vertically Opposite]

$\large{\boxed{\bold{∠7\:=\:135°}}}$

Finding ∠8

➝ ∠6 + ∠8 = 180°

[Linear Pair]

➝ 135° + ∠8 = 180°

➝ ∠8 = 180°-135°

$\large{\boxed{\bold{∠8\:=\:135°}}}$

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Additional Notes :-

★ 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°).

★ 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.

Answer 2

Answer:

if angle 1 is 45 then find measurement of other angles 2,3,6,7,8

all are equal