Question

In this parallelogram find the missing value.​

Answer 1

Answer:

180-75=105 (linear pair)

y = 105 (non adjacent angle of parallelogram are equal)

x+y=180

x+ 105=180

x=180-105

x=75

Answer 2

Given:-

• In //gm PQRS, ∠R = 75°, ∠RSP = x, ∠SPQ = y & ∠PQR = z
• PQ // RS & PS // QR

To Find:-

• The values of x,y & z.

Solution:-

As, PQ//RS & QR as transversal

∠PQR = ∠R [Corresponding Angles]

$\Large{\red{\mathfrak{∴\; z = 75°}}}$

WKT, Opposite Angles in a Parallelogram are Equal.

∠PQR = ∠RSP

$\Large{\green{\mathfrak{∴\;x = 75°}}}$

WKT, In a Parallelogram adjacent angles are Supplementary.

$→\;{\sf{∠PQR+∠SPQ = 180°}}$

$→\;{\sf{75°+y = 180°}}$

$→\;{\sf{y = 180°-75°}}$

$\Large{\blue{\mathfrak{∴\;y = 105°}}}$

Hope It Helps You ✌️