Question

In fig.PQ,RS and UT are parallel lines. i) if c=57 and a=c/3,find the value of d. ii)if c=75 and a=2c/5,find b.​

Answer 1

Given:

PQ, RS and UT are parallel lines

To find:

i) if c=57 and a=c/3,find the value of d.

ii)if c=75 and a=2c/5,find b.​

Solution:

(i) Finding the value of d:

Here → c = 57° and a = $\frac{c}{3}$

∴ a = $\frac{c}{3}$ = $\frac{57}{3}$ = 19°

We have PQ // UT

∴ ∠c = ∠QPT ...... [alternate angles]

Also, ∠QPT = a + b

∴ c = a + b

⇒ 57° = 19° + b

⇒ b = 38°

Now, we have PQ // RS

∠b + ∠d = 180° ..... [∵ when the line are parallel, then the sum of co-interior angles is equal to 180°]

 

Substituting b = 38°, we get

38° + ∠d = 180°

⇒ ∠d = 180° - 38°

⇒ ∠d = 142°

Thus, the value of d = 142°.

(ii) Finding the value of b:

Here → c = 75° and a = $\frac{2c}{5}$

∴ a = $\frac{2c}{5}$ = $\frac{2\:\times\:75}{5}$ = 30°

We have PQ // UT

∴ ∠c = ∠QPT ...... [alternate angles]

Also, ∠QPT = a + b

∴ c = a + b

⇒ 75° = 30° + b

⇒ b = 45°

Thus, the value of b = 135°.

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Answer 2

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Here's your answer mate

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Reflex action✍

The Automatic response of effector to a stimulus is called a reflex action

Examples:

1 withdrawal of hand and touching fire.

2 sneezing coughing or vomiting when nose larynx or pharynx for get irritated by foreign particles.

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