Question

16. In the given figure , the directed lines are parallel to each other.Find the
unknown angles.(give reasons)

Answer 1

Answer:

angle A is 30 degree (coresponding angle)

angle A= angle B ( interior alternate angle) so b =30 degree

angle B = D ( coresponding angles ) d = 30 degree

angle C = 180 - 30 = 150 degree

Answer 2

★ How to do :-

Here, we are given with two lines which are parallel to each other. There is a line passing through them which is called as a transversal line. We are given with the measurement of only one angle in it. The other angles are named as a, b, c and d. We area sked to find the measurements of those angles. Here, the concept of vertically opposite angles, corresponding angles, alternate angles and also that the sum of two angles form 180°, when they form straight line. So, let's solve!!

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➤ Solution :-

We know that the vertically opposite angles are always equal in measurements of degrees. So,

Value of ∠a :-

${\tt \leadsto \orange{\underline{\boxed{\tt \angle{a} = {30}^{\circ}}}}}$

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We know that the alternate angles are always equal in measurements of degrees. So,

Value of ∠b :-

${\tt \leadsto \orange{\underline{\boxed{\tt \angle{b} = {30}^{\circ}}}}}$

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We know that two angles forming a straight line always measures 180° when added. So,

Value of ∠c :-

${\tt \leadsto {30}^{\circ} + \angle{c} = {180}^{\circ}}$

${\tt \leadsto \angle{c} = 180 - 30}$

${\tt \leadsto \orange{\underline{\boxed{\tt \angle{c} = {150}^{\circ}}}}}$

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We know that the corresponding angles always measures the same. So,

Value of ∠d :-

${\tt \leadsto \orange{\underline{\boxed{\tt \angle{d} = {30}^{\circ}}}}}$

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Hence solved !!