Question

In the following figure, AB,
CD and a transversal cuts them. If angle 1 =75 degree, find all other angles.​

Answer 1

Correct question:-

In the following figure, AB || CD and a transversal cuts them. If angle 1= 75 degree, find all other angles.​

Given:-

• AB parallel to CD
• Angle 1 = 75°

To find:-

• All the other angles:- angle 2, 3, 4, 5, 6, 7 and 8

Solution:-

Angle 2 = 75°

Reason: Vertically opposite angles are equal. Hence, Angle 1 = Angle 2.

Angle 8 = 75°

Reason: Corresponding angles are equal. Hence, Angle 1 = Angle 8.

Angle 3 = 75°

Reason: Vertically opposite angles are equal. Hence, Angle 8 = Angle 3.

Angle 4 = 105°

Reason: Angle 3 and Angle 4 are a linear pair which means that the sum of both their measures is 180°. Hence, Angle 4 = 180° - 75° (Angle 3) = 105°

Angle 7 = 105°

Reason: Vertically opposite angles are equal. Hence, Angle 4 = Angle 7.

Angle 5 = 105°

Reason: Corresponding angles are equal. Hence, Angle 7 = Angle 5.

Angle 6 = 105°

Reason: Vertically opposite angles are equal. Hence, Angle 5 = Angle 6.

Answer 2

➤ Given :-

Measurement of angle 1 :- 75°

The transversal cuts the two parellel lines.

➤ To Find :-

Measurements of angle 2 to 8

How to do :-

Here, we are given that a transversal line is passing through two lines which are parellel to each other. And the angle 1 measures 75°. In this question, we can find the answer by using the methods of alternate and corresponding angles.

➤ Solution :-

Here, we will solve one by one

Measurement of angle 2 :-

Here, we know that vertically opposite angles are always equal. So, the angle 2 will be same as the angle 1.

So,

Measurement of angle 2 :- 75°

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Measurement of angle 3 :-

Here, we know that corresponding angles are always equal. So, the angle 3 measures same as the angle 2 :-

So,

Measurement of angle 3 :- 75°

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Measurement of angle 4 :-

Here, we know that one acute and one obtuse angle makes 180°. The line CD is of 180°. So, we can find the measurement of angle 4 by subtracting 180 and the angle 3.

${\tt 180 - 75}$

${\tt 105 ^{\circ}}$

So,

Measurement of angle 4 :- 105°

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Measurement of angle 5 :-

Here, we know that one acute and one obtuse angle makes 180°. The line CD is of 180°. So, we can find the measurement of angle 5 by subtracting 180 and the angle 1.

${\tt 180 - 75}$

${\tt 105 ^{\circ}}$

So,

Measurement of angle 5 :- 105°

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Measurement of angle 6 :-

Here, we know that alternate angles are always equal. So, we can find the value of angle 6.

So,

Measurement of angle 6 :- 105°

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Measurement of angle 7 :-

Here, we know that corresponding angles are always equal. So, we can find the value of angle 7.

So,

Measurement of angle 7 :- 105°

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Measurement of angle 8 :-

Here, we know that corresponding angles are always equal. So, we can also find the value of angle 8 :-

So,

Measurement of angle 8 :- 75°

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More to know :-

• Alternate angles are the angles which are opposite to each other. They always measure same measurements. They can also be classified as vertically opposite angles.
• Corresponding angles are the angles in which one angle will be in the interior of the parallel lines and the other will be in exterior. The interior and exterior in RHS are classified separate corresponding angles and the interior and exterior angles in LHS are classified as separate corresponding angles.
• If any one of the quality fits correctly to the lines, they are classified as parellal lines.