In the given figure, sides QP and SR of quadrilateral PQRS are respectively extended to point Y and X. Value of x is
degree.
Answers
Linear pair of angles:
If Non common arms of two adjacent angles form a line, then these angles are called linear pair of angles.
Axiom- 1
If a ray stands on a line, then the sum of two adjacent angles so formed is 180°i.e, the sum of the linear pair is 180°.
Axiom-2
If the sum of two adjacent angles is 180° then the two non common arms of the angles form a line.
The two axioms given above together are called the linear pair axioms.
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Solution:
Given,
∠SPR = 135° and ∠PQT = 110°
A.T.Q
∠SPR +∠QPR = 180° (by Linear pair axiom.)
⇒ 135° +∠QPR = 180°
⇒ ∠QPR = 180° - 135°
⇒ ∠QPR = 45°
∠PQT +∠PQR = 180° (by Linear pair axiom.)
⇒ 110° +∠PQR = 180°
⇒ ∠PQR = 70°
Now,
∠PQR +∠QPR + ∠PRQ = 180° (Sum of the interior angles of the triangle.)
⇒ 70° + 45° + ∠PRQ = 180°
⇒ 115° + ∠PRQ = 180°
⇒ ∠PRQ = 65°
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