The length of each leg of an isosceles triangle is 4cm less than twice the base. the perimeter of the triangle is 17 cm. find the measure of each side of the triangle.

The base = 5, The legs are 6 each.

Step-by-step explanation:

Let the Base=x, Let the legs = (2x-4)

Perimeter = sum of all the sides = x + (2x-4) + (2x-4) = 5x-8 when you combine the like terms.

You know that the Perimeter = 17 cm. So, 17=5x-8.

Now you can solve for x. Once you do that, you can put your value of x into the leg equations.

17=5x-8

17+8=5x-8+8

25=5x

x=5

The Base is x=5 cm long, The Legs are each 2x-4=2(5)-4=10-4=6 cm long.

The Perimeter is x + (2x-4) + (2x-4) = 5 + 6 + 6 = 17.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32