Verified answer

Step-by-step explanation:

(8) Let the angles of the triangle be x, y, z

x=y+z

x+y+z= 180 (Angle sum property of a triangle)

Put y+z in place of x

y+z+y+z=180

2(y+z) = 180

y+z=90

as we took x = y+z

then x=90

(11) Yes it is possible to construct a triangle with sides 8cm, 7cm and 9cm

As 8+7= 15

and 15 > 9

it satisfies the statement that sum of two sides of a triangle is greater than 3rd side

(12)

Angle sum property of triangle= 180

In ∆PQR

55° + 45° + 35° + a = 180°

135° + a = 180°

a= 180°-135°= 45°

Now in ∆PSR

35 + 45 + x = 180°

80°+x= 180°

x = 100°

Now the straight line QPT

35° + 45° +y =180°

y=100°

Answer:

step 1-let X=90°

step 2-in triangle SPR add all angles

90°+45°=180°

x+135°=180°

x=180°-135°

=45°

step 3-on line QPT add all angles of QPT

y+35°+45°=180°

y=180°-80°

y=100°

x=90°