Question

answer this question with steps

Answer 1

Given:

• ∠TPV = 30°
• ∠PRS = 110°
• ∠PQR = x°

To Find:

• ∠PQR = ??

Process:

To find the value of x° we first have to find the values of ∠QPR and ∠PRQ. So, PRQ is a triangle whose sum of all angles is 180°(angle sum property of triangle). So, we can create an equation as follows: ∠QPR + ∠PRQ + ∠PQR = 180°. After solving the equation we get the value of x°.

Solution:

∠QPR = ∠TPV = 30° [vertically opp. angles]

∠PRQ + ∠PRS = 180° [linear pair]

∠PRQ + 110° = 180°

∠PRQ = 180° - 110°

∠PRQ = 70°

As we can see PRQ is a triangle. So, the sum of all its angle is 180°(angle sum property of triangle). Thus,

∴ ∠QPR + ∠PRQ + ∠PQR = 180°

⇒ 30° + 70° + x° = 180°

⇒ 100° + x = 180°

⇒ x° = 180° - 100°

⇒ x° = 80°

Hence, x° = 80°.

Answer 2

Answer:

X=80° is the correct answer