Solve the following problems: △abc ∼ △a1b1c1. find angle measures x, y, z, w

Therefore angle measure are

Step-by-step explanation:

Given:

△ABC ∼ △A1B1C1.

∠A = 60°

∠B1 = 50°

∠B =x , ∠C = y , ∠A1 = z , ∠C1 = w

To Find:

angle measures,

x = ?, y = ? ,z = ?, w = ?

Solution:

△ABC ∼ △A1B1C1.  .............Given:

If two triangles are similar then the corresponding angles of similar triangles are congruent.

∴ ∠A ≅ ∠A1          .............1

  ∠B ≅ ∠B1          .............2

 ∠C ≅ ∠C1           .............3

But ,∠A = 60° ,∠B1 = 50° given

∴ ∠A ≅ ∠A1 = 60° ................Transitive Property

  ∠B ≅ ∠B1  = 50° ................Transitive Property

Therefore

∠B =x = 50°,  ∠A1 = z = 60° ,

Now,

In a Triangle sum of the measures of all the angles of a triangle is 180°.

In ΔABC we have

Substituting the given value we get

m∠C = y = 70°

But   ∠C ≅ ∠C1           ............From 3

∴ ∠C1 = w = 70° ................Transitive Property

Therefore angle measure are

it is x=-4

step-by-step explanation:

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240