Question

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Answer 1

Answer:

• 60° is the required value of x .

Step-by-step explanation:

According to the Question

It is given that,

• Angle PQB = 5y
• Angle QPB = 45°
• Angle PBQ = x

Firstly we calculate the value of y .

As we know that sum of linear pair of angle is 180°

↠ 7y + 5y = 180°

↠ 12y = 180°

↠ y = 180°/12

↠ y = 15°

Now, putting the value of y

→ 5y = 5×15 = 75°

→ 7y = 7×15 = 105°

Now, In ∆PQB

Sum of all angles in a triangle is 180°

↠45° + 75° + x = 180°

↠ 120 + x = 180°

↠ x = 180° - 120°

↠ x = 60°

• Hence, the value of x is 60°.

Option D) 60° is the correct .

Answer 2

Answer : D) 60°

First, find the value of y

↣7y + 5y = 180° (Linear Pair)

↣12y = 180°

↣y = 180/12

↣ y = 15

Therefore, the measure of the angles

• 7y = 7×15 = 105°
• 5y = 5×15 = 75°

Now, finding the value of x

↣ 45° + 5y + x = 180°

(sum of all angles in a triangle)

↣ 45° + 75° + x = 180°

↣ 120 + x = 180

↣ x = 180 - 120

↣ x = 60°

⚘ Properties used:

• Angle Sum Property
• Linear Pair

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