Question

In the given figure . PQ = PR , SPR = 100
then pQR is equal to?​

Answer 1

Answer:

50

Step-by-step explanation:

SPR=PQR+PRQ

100=2PQR [As PQ=PR, so According to triangle property PQR=PRQ]

SO, PQR=50

Answer 2

$\Large{\underline{\bf{Given:}}}$

☞ PQR is a Triangle & PQ is extended to S

☞ PQ = PR

☞ ∠SPQ is the exterior angle of the ∆le which measures $100$

$\Large{\underline{\bf{To\;Find:}}}$

☞ ∠PQR

$\huge{\underline{\underline{\bf{Solution:}}}}$

In ∆PQR, ∠PQR = ∠PRQ

As, Angles Opposite To Equal Sides (PQ = PR) Are Equal In A Triangle.

So, Let ∠PQR = ∠PRQ = x° ➝ (1)

W.K.T

Exterior Angle = Sum of Two Opposite Interior Angles

$→\;{\sf{∠PQR+∠PRQ = 100°}}$

$→\;{\sf{x+x = 100°}}$

$→\;{\sf{2x = 100°}}$

$→\;{\sf{x = \frac{100°}{2}}}$

$➝\;{\bf{x = 50°}}$

$\Large{\green{\underline{\underline{\tt{AnSweR:}}}}}$

Value of ∠PQR ◕➜ $\huge{\red{\mathfrak{50°}}}$

Hope It Helps You ✌️