Question

S and R are points on the circumference of the semicircle described on diameter PQ. if PS= SR and angle SPQ= 56 degree calculate angle PQS and angle PQR​

Answer 1

Answer:

${\boxed{<PQS = 34^{o} }$  

Step-by-step explanation:

Given:

• PS= SR,

• ∠SPQ = 56°

To Find:

∠PQS and∠ PQR​ = ?

Solution:

Note:  ∠PSQ= 90°  (since : A triangle inscribed in a

                           semi circle  is a right triangle)

In Δ SPQ,

∠SPQ + ∠PQS + ∠PSQ = 180°    (Angle Sum Property)

56° + ∠PQS + 90° = 180°  

⇒ ∠PQS + 146° = 180°

⇒ ∠PQS  = 180°- 146°

⇒${\boxed{<PQS = 34^{o} }$  

Answer 2

Answer:

PQS=34

Step-by-step explanation:

Given:

PS= SR,

∠SPQ = 56°

To Find:

∠PQS and∠ PQR​ = ?

Solution:

Note:  ∠PSQ= 90°  (since : A triangle inscribed in a

                          semi circle  is a right triangle)

In Δ SPQ,

∠SPQ + ∠PQS + ∠PSQ = 180°    (Angle Sum Property)

56° + ∠PQS + 90° = 180°  

⇒ ∠PQS + 146° = 180°

⇒ ∠PQS  = 180°- 146°

⇒  PQS=34