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

the correct is answer is a 9-sided polygon!

step-by-step explanation:

this is not possible to solve with the info given.   you need at least an one angle somewhere.