Mathematics

In the diagram above, |PQ| = |PR| = |RS| and ∠RPS = 32°. Find the…

In the diagram above, |PQ| = |PR| = |RS| and ∠RPS = 32°. Find the value of ∠QPR

  • A.
    72o
  • B.
    64o
  • C.
    52o
  • D.
    32o
  • E.
    26o
Correct Answer: Option C
Explanation

From the figure, < PSR = 32° (base angles of an isos. triangle)

(therefore) < PRS = 180° – (32° + 32°) = 116° (sum of angles in a triangle)

< QRP = 180° – 116° = 64° (angle on a straight line)

< PQR = 64° (base angles of an isos. triangle)

< QPR = 180° – (64° + 64°) = 52°