Question

pla answer these 2 questions......​

Answer 1

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❇ Required Answers:

✏ GiveN:

Q.1) In $\triangle$ PQR, $\angle$ R > $\angle$Q, Then which condition is true?

Q.2) Two angles measure (a - 60)° and (123 - 3a)°. They ar opposite to equal sides of an isoceles triangle, find value of a.

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❇ How to solve?

The question is based on basic properties of triangle.

✏ The relationship between the sides and opposite angles. Largest side is opposite to largest opposite angle and smaller side is opposite to corresponding opposite smallest angle. Equal or same sides have equal angles opposite to them.

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❇ Solution:

1) $\triangle$ PQR, $\angle$ R > $\angle$Q,

✏ We know, larger side is opposite to larger angle and smaller side is opposite to smaller angle. Refer to the attachment...So, here,

• Opposite side to $\angle$ R = PQ
• Opposite side to $\angle$ Q = PR

According to question,

➙$\angle$ R > $\angle$ Q

➙ PQ > PR

So, Correct option is B

2) Here, we have two angles (a - 60)° and (123 - 2a)°.

✏ We know, equal angles are opposite to equal angles. Here, These are the two equal angles of isoceles triangle because they are opposite to equal sides. So,

➙ a - 60° = 123° - 2a

➙ a + 2a = 123° + 60°

➙ 3a = 183°

➙ a = 183/3 = 61°

So, Answer is 61°.

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Answer 2

Answer:

1) △ PQR, ∠ R >∠ Q,

☸ Larger side is opposite to larger angle and smaller side is opposite to smaller angle. Refer to the attachment.

Then,

❇Opposite side to ∠ R = PQ

❇Opposite side to ∠ Q = PR

According to question,

↪∠ R > ∠ Q

↪ PQ > PR

So, Correct option is B

2) Here, we have two angles (a - 60)° and (123 - 2a)°.

☸ Equal angles are opposite to equal angles. Here, These are the two equal angles of isoceles triangle because they are opposite to equal sides. So,

↪a - 60° = 123° - 2a

↪a + 2a = 123° + 60°

↪ 3a = 183°

↪ a = 183/3 = 61°

Thus, Answer is 61°.