Question

5. In fig. 24.18, ∆PQR is an equilateral triangle

Fig. 24.18
Find the values of x,y and z.​

Answer 1

Step-by-step explanation:

Given:-∆PQR is an equilateral triangle

then,angle PQR=60°,PRQ=60°,RPQ==60°

TO FIND:-x,y,z

now,A/q

By exterior angle prop. of ∆PQR

angle PRT=PQR+RPQ

=60°+60°

=120°

z=120°

similarly,angle PQS=120°

now,In∆PRT,

PRT+PTR+RPT=180°

120°+30°+y=180°

150°+y= 180°

y=180°-150°

y=30°

now,IN∆PQS

PQS+PSQ+SPQ=180°

120°+40°+x=180

160°+x= 180°

x=180°-160°

x= 20°

Hence,x=20°,y=30°,z=120°

Answer 2

Answer:

It's very easy firstly you have to the properties of equilateral triangle that is in equilateral triangle all sides and all angles are equal to 60.

So angle p and q and r will be 60.

Now, in triangle TPS

Angle T + angle P + angle S = 180

30+angle p + 40 = 180

70 + angel P = 180

Angle P = 180-70

Angle P = 110

So x = 110 - 60 = 50

Y = 110-60=50

So z =180- y + angle PTR

Z = 180-50+30

Z = 180-80

Z = 100

So x =50, y = 50, z = 100.

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