Question

5 In the given figure line r ∥ line s and line t ∥ line u. Find the measure of ∠a, ∠b and ∠c from the information provided.explanation bhe do​

Answer 1

★ Solution :-

We know that the vertically opposite angles measures same. So, the measure of ∠c will be the same as 3x+20.

We know that, the interior angles on same side of transversal measures up to 180°. So,

$\sf \leadsto (3x + 20) + (2x + 10) = {180}^{\circ}$

$\sf \leadsto 3x + 2x + 20 + 10 = {180}^{\circ}$

$\sf \leadsto 5x + 20 + 10 = {180}^{\circ}$

$\sf \leadsto 5x + 30 = {180}^{\circ}$

$\sf \leadsto 5x = 180 - 30$

$\sf \leadsto 5x = 150$

$\sf \leadsto x = \dfrac{150}{5}$

$\sf \leadsto x = 30$

Now, let's find the measures of all unknown angles.

Measurement of ∠c :-

$\sf \leadsto 3x + 20$

$\sf \leadsto 3(30) + 20$

$\sf \leadsto 90 + 20$

$\sf \leadsto \angle{c} = {110}^{\circ}$

Measurement of ∠a :-

$\sf \leadsto \angle{a} + \angle{c} = {180}^{\circ}$

$\sf \leadsto \angle{a} + {110}^{\circ} = {180}^{\circ}$

$\sf \leadsto \angle{a} = 180 - 110$

$\sf \leadsto \angle{a} = {70}^{\circ}$

Measurement of ∠b :-

$\sf \leadsto \angle{a} + \angle{b} = {180}^{\circ}$

$\sf \leadsto {70}^{\circ} + \angle{b} = {180}^{\circ}$

$\sf \leadsto \angle{b} = 180 - 70$

$\sf \leadsto \angle{b} = {110}^{\circ}$

Therefore, the measurements of angles a, b and c are 70, 110 and 110 degrees respectively.

Answer 2

★ Solution ↓

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→ In the given figure, we can see that Angle C is vertically opposite angle and therefore, it will also measure the same that is 3x + 20.

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→ Now, we are having 2 interior angles on same side of transversal and we know that the sum of 2 such angles is always 180°.

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→ (3x + 20) + (2x + 10) = 180°

→ 3x + 20 + 2x + 10 = 180°

→ 3x + 2x + 20 + 10 = 180°

→ 5x + 30 = 180°

→ 5x = (180 - 30)°

→ 5x = 150°

→ x = $\frac{150}{5}$

→ x = 30

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→ Value of x = 30

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★ Measurement of Angle C :-

→ 3x + 20

→ 3(30) + 20

→ 90 + 20

→ Angle C = 110°

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★ Measurement of Angle A :-

→ Sum of two interior angles on same side of transversal is always 180°

→ Angle A + Angle C = 180°

→ Angle A + 110° = 180°

→ Angle A = (180 - 110)°

→ Angle A = 70°

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★ Measurement of Angle B :-

→ Sum of two interior angles on same side of transversal is always 180°

→ Angle A + Angle B = 180°

→ 70° + Angle B = 180°

→ Angle B = (180 - 70)°

→ Angle B = 110°

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Therefore,

Angle A = 70°

Angle B = 110°

Angle C = 110°

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