Math, asked by dhillongarry980, 7 months ago

29. AB is a diameter of the circle APBR as shown
in the figure. APQ and RBQ are straight lines.
Find :
(i) PRB,
P
(ii) PBR,

(iii) BPR


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Answers

Answered by ParvezShere
0

(i)  ∠PRB = 35°

(ii) ∠PBR = 115°

(iii) ∠BPR = 30°

Given:

AB is the diameter of the circle.

APQ and RBQ are straight lines.

∠PAB = 35°

∠PQB = 25°

To find:

(i)  ∠PRB

(ii) ∠PBR

(iii) ∠BPR

Solution:

Now,

in triangle PAB and triangle PRB

∠PAB = ∠PRB = 35°  ( angles in the same segment of a circle are equal)

∴ ∠PRB = 35°

Also, in triangle BAP,

∠APB = 90°  (the angle in a semi-circle is always a right angle)

∠APB + ∠BPQ = 180° ( by linear pair)

putting the value of ∠APB in the above equation,

90° + ∠BPQ = 180°

⇒∠BPQ = 180° - 90°

⇒∠BPQ = 90°

Now, in triangle PQR, we have

∠PQR + ∠PRQ + ∠RPQ = 180° (by angle sum property of triangle)

putting values of ∠PQR = 25° and ∠PRQ = 35°

25° + 35° + ∠RPQ = 180°

⇒ 60° + ∠RPQ = 180°

⇒∠RPQ = 180° - 60°

⇒∠RPQ = 120°

∴ ∠BPR + ∠BPQ = ∠RPQ

⇒∠BPR = ∠RPQ - ∠BPQ

⇒∠BPR = 120° - 90°

⇒∠BPR = 30°

in triangle PBR,

∠PBR + ∠BRP + ∠BPR = 180°  ( angle sum property of triangle)

putting the values of  ∠BRP = 35° and ∠BPR = 30°

∠PBR + 35° + 30° = 180°

∠PBR =  180° - (35° + 30°)

∠PBR = 180° - 65°

∠PBR = 115°

#SPJ1

Answered by Rameshjangid
0

Answer: ∠PRB = 35°, ∠PBR = 115° and ∠BPR = 30°

Given:

  • AB is the diameter of the circle.
  • APQ and RBQ are straight lines.
  • ∠PAB = 35°
  • ∠PQB = 25°

To find:

  1. ∠PRB
  2. ∠PBR
  3. ∠BPR

Step-by-step explanation:

Step 1: Now, in triangle PAB and triangle PRB

∠PAB = ∠PRB = 35°  (angles in the same segment of a circle are equal)

∴ ∠PRB = 35°

Also, in triangle BAP,

∠APB = 90°  (the angle in a semi-circle is always a right angle)

∠APB + ∠BPQ = 180° ( by linear pair)

putting the value of ∠APB in the above equation,

90° + ∠BPQ = 180°

⇒∠BPQ = 180° - 90°

⇒∠BPQ = 90°

Step 2: Now, in triangle PQR, we have

∠PQR + ∠PRQ + ∠RPQ = 180° (by angle sum property of triangle)

putting values of ∠PQR = 25° and ∠PRQ = 35°

25° + 35° + ∠RPQ = 180°

⇒ 60° + ∠RPQ = 180°

⇒∠RPQ = 180° - 60°

⇒∠RPQ = 120°

∴ ∠BPR + ∠BPQ = ∠RPQ

⇒∠BPR = ∠RPQ - ∠BPQ

⇒∠BPR = 120° - 90°

⇒∠BPR = 30°

Step 3: In triangle PBR,

∠PBR + ∠BRP + ∠BPR = 180°  ( angle sum property of triangle)

putting the values of  ∠BRP = 35° and ∠BPR = 30°

∠PBR + 35° + 30° = 180°

∠PBR =  180° - (35° + 30°)

∠PBR = 180° - 65°

∠PBR = 115°

For more questions follow the given link below.

https://brainly.in/question/45571762

https://brainly.in/question/44497962

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