Question

In figure, PQ = PS. The value of x is​

Answer 1

Answer:

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Answer 2

Given:-

• In the given figure PQ = PS
• ∠Q = 110°

To Find:-

• The value of x [∠RPS]

Note:-

• Refer to the attachment for clear view of explanation.

Before solving:-

• Let us name the unknown angle with y

Solution:-

In the given figure,

There are two triangles,

1st ∆PQS which is an isosceles triangle who two sides and angles are equal.

2nd ∆PSR which is a scalene triangle.

Also in the figure,

∠PQY = 110°

So,

∠PQY + ∠PQS = 180° [Linear Pair]

= 110 + ∠PQS = 180°

=> ∠PQS = 180° - 110°

=> ∠PQS = 70°

Now,

In ∆PQS

PS = PQ

Therefore,

∠PSQ = ∠PSQ = 70°

Now,

In The figure again,

∠PSQ + ∠PSR = 180° [Linear Pair]

70° + ∠PSR = 180°

=> ∠PSR = 180° - 70°

=> ∠PSR = 110°

Therefore,

Now,

In ∆PSR,

∠PSR = 110°

∠SPR = x

∠PRS = 25°

According to angle - sum property of the triangle

∠PSR + ∠SPR + ∠PRS = 180°

= 110° + x + 25° = 180°

=> 135° + x = 180°

=> x = 180° - 135°

=> x = 45°

Therefore the value of x is 45° (option 2)

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Explore More!!

→ What is angle - sum property of a triangle?

✓ The angle - sum property of a triangle states that the sum of all angles of a triangle is always 180°

✭ The linear pair is always supplementary (180°)

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