Question

In the figure, I and m are parallel lines and t is transversal. If L3= 75°,
find the measures of all the other angles.​

Answer 1

★ How to do :-

Here, we are given with two lines that are parellel to each other. A line is passing through them called as transversal line. The transversal line is named as t and the other lines as l and m. The ∠3 measures 75°. We are asked to find the value of all the other seven angles in that figure. So, we are going to use the concepts of vertically opposite angles, linear pair of angles, alternate angles and also corresponding angles. So, let's solve!!

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➤ Solution :-

We know that the veryically opposite angles measures same in measurements of degrees. So,

Value of ∠1 :-

${\tt \leadsto \orange{\boxed{\tt \angle{1} = {75}^{\circ}}}}$

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We know that linear pairs of angles measures 180° when added together. So,

Value of ∠2 :-

${\tt \leadsto 75 + \angle{2} = {180}^{\circ}}$

${\tt \leadsto \angle{2} = 180 - 75}$

${\tt \leadsto \orange{\boxed{\tt \angle{2} = {105}^{\circ}}}}$

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We know that linear pair of angles measure 180° when added together. So,

Value of ∠4 :-

${\tt \leadsto 75 + \angle{4} = {180}^{\circ}}$

${\tt \leadsto \angle{4} = 180 - 75}$

${\tt \leadsto \orange{\boxed{\tt \angle{4} = {105}^{\circ}}}}$

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We know that the corresponding angles always measures the same in measurements of degrees. So,

Value of ∠5 :-

${\tt \leadsto \orange{\boxed{\tt \angle{5} = {105}^{\circ}}}}$

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We know that the corresponding angles always measures the same in measurements of degrees. So,

Value of ∠6 :-

${\tt \leadsto \orange{\boxed{\tt \angle{6} = {75}^{\circ}}}}$

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We know that the vertically opposite angles always measures same in measurements of degrees. So,

Value of ∠7 :-

${\tt \leadsto \orange{\boxed{\tt \angle{7} = {105}^{\circ}}}}$

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We know that the vertically opposite angles always measures same in measurements of degrees. So,

Value of ∠8 :-

${\tt \leadsto \orange{\boxed{\tt \angle{8} = {75}^{\circ}}}}$

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Hence solved !!