Question

please answer this question ​

Answer 1

★ How to do :-

Here, we are given with three figures in which we are asked to find that whether those two lines are forming a pair of parallel line. For finding this, we usr some other concepts such as corresponding angles, straight line angle measures 180° and also alternate angles. These are mainly to be applied whether the lines form a parallel line or not. In the other question, we are given with the ratio of all the angles of a triangle. We are asked to find the measurement of all the three angles. So, let's solve!!

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➤ Solution (1) :-

Any angle which forms straight line always measures 180°. So, the angle corresponded to the angle of 60° measures,

${\tt \leadsto x + 120 = 180}$

Shift the number 120 from LHS to RHS, changing it's sign.

${\tt \leadsto x = 180 - 120}$

Subtract the values on RHS to get the value of x.

${\tt \leadsto x = {60}^{\circ}}$

We know that two angles that are corresponding to each other always measures the same.

${\tt \leadsto {60}^{\circ} = {60}^{\circ}}$

${\large \sf \pink{\boxed{\sf It \: can \: form \: a \: parallel \: line}}}$

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➤ Solution (2) :-

Any angle which forms straight line always measures 180°. So, the angle alternate to the angle of 60° measures,

${\tt \leadsto x + 60 = 180}$

Shift the number 60 from LHS to RHS, changing it's sign.

${\tt \leadsto x = 180 - 60}$

Subtract the values on RHS to get the value of x.

${\tt \leadsto x = {120}^{\circ}}$

The value of x should be same as it's alternate angle measuring 60°. But, is not the same. So,

${\large \sf \pink{\boxed{\sf It \: cannot \: form \: a \: parallel \: line}}}$

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➤ Solution (3) :-

Any angle which forms straight line always measures 180°. So, the angle corresponded to the angle of 133° measures,

${\tt \leadsto x + 47 = 180}$

Shift the number 60 from LHS to RHS, changing it's sign.

${\tt \leadsto x = 180 - 47}$

Subtract the values on RHS to get the value of x.

${\tt \leadsto x = {133}^{\circ}}$

We can see that both angles measure 133°. So,

${\large \sf \pink{\boxed{\sf It \: can \: form \: a \: parallel \: line}}}$

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➤ Solution (4) :-

${\tt \leadsto 2 : 3 : 4 = {180}^{\circ}}$

Insert a variable x after each part of ratio and also insert addition sign.

${\tt \leadsto 2x + 3x + 4x = 180}$

Add all the values having the same variable.

${\tt \leadsto 9x = 180}$

Shift the number 9 from LHS to RHS, changing it's sign.

${\tt \leadsto x = \dfrac{180}{9}}$

Simplify the fraction to get the value of x.

${\tt \leadsto x = {20}^{\circ}}$

Measure of ∠1 :-

${\tt \leadsto 2x = 2 \times 20}$

${\tt \leadsto \angle{1} = {40}^{\circ}}$

Measure of ∠2 :-

${\tt \leadsto 3x = 3 \times 20}$

${\tt \leadsto \angle{2} = {60}^{\circ}}$

Measure of ∠3 :-

${\tt \leadsto 4x = 4 \times 20}$

${\tt \leadsto \angle{3} = {80}^{\circ}}$

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Hence solved !!