Maths-
General
Easy
Question
Find the values of x, y and z.
Hint:
Two congruent triangles have the same size and shape ,the corresponding angles (or) sides are congruent (equal) .Using congruence find value of x . Find value of y using sum of angles on straight line.Find the value of z by using the sum of angles in the triangle as 
The correct answer is: x = 30 ;y = 100 and z = 100
Step 1:- Find congruence of triangles
Given ,LM = QP(given in diagram)
MP = PR(given in diagram)
PL = RQ(given in diagram)
By SSS rule,
We get ΔLMP ≅ ΔQPR
Step 2:- Using congruence find value of x
The angles in similar triangles are equal then We get ,
∠MPL = ∠PRQ 50° = ∠PRQ
∠LMP = ∠QPR 30° = x° x = 30 (values of both angles are given in diagram )
Step 3:- Find value of y using sum of angles on straight line
We know sum of angles on a straight line is 180°
So, ∠LPM +∠LPQ +∠QPR = 180° (substitute values given in diagram)
x + y + 50 = 180 (substitute x =30)
y + 80 =180 
y= 100
Step 4:-Find the value of z by using the sum of angles in the triangle as 180°.
∠QPR +∠PQR +∠PRQ = 180°
x + z +∠PRQ = 180°
We get 50° = ∠PRQ ,and x = 30 in step 2
30 + z +50 = 180°
z = 100
∴ x = 30 ,y = 100 and z = 100
Step 3:- Find value of y using sum of angles on straight line
We know sum of angles on a straight line is 180°
So, ∠LPM +∠LPQ +∠QPR = 180° (substitute values given in diagram)
y= 100Step 4:-Find the value of z by using the sum of angles in the triangle as 180°.
We get 50° = ∠PRQ ,and x = 30 in step 2
∴ x = 30 ,y = 100 and z = 100
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