Question
Download Solution PDFIn the given figure, MN = RM = RP, then what is the value (in degrees) of ∠MPR?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFHere, ΔPRM and ΔMRN are isosceles triangles
Also, in ΔRPN
⇒ ∠RPM + ∠RNP = 102° ….(i) [EXTERIOR ANGLE PROPERTY]
⇒ ∠MRN = ∠MNR
⇒ ∠MRN + ∠MNR = ∠RMP …(ii) [EXTERIOR ANGLE PROPERTY
⇒ 2∠RNP = ∠RMP = ∠RPM
By (i) and (ii), we get
⇒ 3/2(∠RPM) = 102°
⇒ ∠RPM = 68°
∴ the correct option is 2)
Alternate Method
Let ∠RNP = x and ∠RPN = y.
Now 102° = x + y.....(i) [EXTERIOR ANGLE PROPERTY]
In triangle RNM,
2x = y …(ii) [EXTERIOR ANGLE PROPERTY
Now add both
3x = 102
x = 34.
We need to find ∠MPR = y = 2x = 2 × 34 = 68°
Last updated on Jul 21, 2025
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