Question

M angles = (x+4) and m angle Q = (5x-4)

Answer 1

Answer:

It is given that the measures of the angles of triangle QRS are m∠Q=2x+4, m∠R=4x−12 and m∠S=3x+8 and also we know that the sum of the measures of the angles of a triangle is 180.

Therefore, 2x+4+4x−12+3x+8=180

⇒9x=180

⇒x=20

Substitute the value of x in the measures of the angles that is:

m∠Q=2(20)+4=44

⇒m∠R=4(20)−12=68

⇒m∠S=3(20)+8=68

Therefore, △QRS is isosceles and QR=QS which means

y+9=3y−13

⇒3y−y=13+9

⇒2y=22

⇒y=11

Now consider the sum of the sides that is:

QR+RS+QS=y+9+2y−7+3y−13=6y−11

Hence, the perimeter of triangle QRS is:

6y−11=6(11)−11=66−11=55