Question

please tell me what is the answer​

Answer 1

Answer:

i) ∠PQR and ∠PRQ = 75°

ii) ∠SQR and ∠SRQ = 55°

iii) x = 20°

Step-by-step explanation:

i) Find, ∠PQR and ∠PRQ

△PQR is a isosceles triangle.

∠PQR = ∠PRQ ( angle opposite to equal side of triangle are equal )

Let,

∠PQR = ∠PRQ = y

∠PRQ + ∠PQR + ∠QPR = 180° ( sum of angles in a triangle is 180°)

y + y + 30° = 180°

2y + 30° = 180°

2y = 180° - 30°

2y = 150°

y = 150°/2

y = 75°

∠PQR = ∠PRQ = ∠y = 75°

ii) Find, ∠SQR and ∠SRQ

△SQR is a isosceles triangle.

∠SQR = ∠SRQ ( angle opposite to equal sides of triangle are equal )

Let,

∠SQR = ∠SRQ = z

∠SQR + ∠SRQ + ∠QSR = 180° ( sum of angles in a triangle is 180°)

z + z + 70° = 180°

2z + 70° = 180°

2z = 180° - 70°

2z = 110°

z = 55°

∠SQR = ∠SRQ = ∠z = 55°

iii) Find x

∠PQS = x

∠PQS + ∠SQR = ∠PQR

x + 55° = 75°

x = 75° - 55°

x = 20°