Question

In the following figure, PQ || SR, SA || BQ and PDS = 480. Find (RCB, X, y.

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Answer 1

Answer:

• x = 48°
• y = 132°
• ∠RCB = 132°

Explanation:

In the figure,

PQ || SR, SA || BQ and ∠PDS = 48°

Here, in PQ || SR, DS is transversal.

∴ x = 48° [∵ Alternate interior angles]

Now,

→ x + y = 180°

Substituting ‘x’ :-

→ 48° + y = 180°

→ y = 180° - 48°

→ y = 132°

And also,

∠RCB = y [∵ Vertically opposite angles]

∴ y = 132°

________________________

Answer 2

★ Solution :-

Since, PQ ll SR,

Therefore,

= > x = 48°

( Alternate interior angles measure the same)

Now,

=> x + y = 180° ( Adjacent angles sum up to 180°)

Now, we will substitute the derived value of "x" in the equation to obtain the value of "y",

Therefore,

=> x + y = 180°

=> 48° + y = 180°

=> y = 180° - 48°

=> y = 132°

Also, ∠y = ∠RCB ( Vertically opposite angles)

Therefore,

∠y = ∠RCB = 132°

★ Answer :-

1. x = 48°

2. y = 132°

3. ∠RCB = 132°

☆ Know More :-

• Sum of adjacent angles is 180°
• Vertically opposite angles measure the same.
• Alternate angles ( maybe exterior or interior) measure the same.

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