Question

in the adjoining figure pQ=pR And mn ||Qr ifQ=60°find the value of X and y ​

Answer 1

Step-by-step explanation:

if p q = pr then

so angle Q = R = 60°

then angle y = 180 - Q + R

then y = 180 - 60 + 60

y = 180- 120

y = 60

and if mn || QR then

angle x = angle R and angle M = angle Q

so x = Q = 60°

then x = 60°

so angle x and y = 60°

hope it helps

be brainly

Answer 2

Answer:

x=y=60°

Step-by-step explanation:

I have explained through 2 methods,

it you are of high school then the first one is for you and if you are of secondary school then the second method below will be helpfull to you.

pq=pr (given)

now, ∆pqr is an isosceles triangle.

so, angle Q = angle R

(because in an isosceles triangle, angles opposite to equal sides are equal)

mn||qr (given)

so, pq is transversal line on parallels mn and qr.

now, angle q = angle m

(corresponding angles are equal)

so, angle m =60°

If a line is drawn parallel to one side intersecting other to sides in distinct points, then the other two sides are divided in the same ratio.

so, mn is intersecting at pq and pr.

now, it is divided into same ratio say, PM and PN.

So, triangle PMN is an isosceles triangle because pm=pn.

now, the opposite angles will be also equal.

so, angle m = angle x

angle x = 60°.

the sum of the interior angles of a triangle is 180°.

so, y+x+m =180°

= y+60°+60°= 180°

= y = 180°- 120°

= y = 60°

hence, x= 60° and y= 60°

there is a second method also:

if mn||qr and pq=pr

then, pq is an isosceles triangle,

So, opposite angles will be equal.

so, angle q = angle r.

now, r = 60°

and q = 60°

corresponding angles are equal,

pq and pr are the transversal on mn||qr,so, we can write, q = r = m = n = 60°

, now n = x

so, x= 60°

and, sum of interior angles of a triangle are 180°,

So, x+ y + m = 180°

=60°+ y+60°=180°

=120°+y=180°

= y = 180°-120°

= y = 60°

hence, x = 60° and y = 60°

I hope it will be helpfull !