Question

Need Expert Answer Asap! Solve For X,Y,Z.

Answer 1

x=65

y=6

z=146

Explanation:

x=65

Triangle angles add up to 360.

We need at least 2 angles to find the missing angle

The lines show congruency between the two triangles, so we know the blank angle on the left triangle is 81. Another way to prove this is the vertical angles theorem, which states vertical angles are congruent. The angle labeled 81 is congruent to the blank angle on the left triangle.

Since we have 2 angles of the left triangle, we can find the third.

180-34-81=65

y=6

Using the evidence from the congruency lines (I call them that), we can tell that the y side is equal to the side labeled 6. If you flipped both triangles the same way you could also tell they are both 6 for that side

z=146

the 34 degree and z angle make a linear pair.

Linear pair=180 degrees

180-34=146, z is 146

Answer 2

x = 65

y = 6

z = 115

Explanation:

For these, we can use theorems and/or sine, cosine, or tangent to solve for x, y, and z.

We know that 34 degrees is congruent to the other angle.

We also know that triangles' angles add up to 180 degrees.

180 - 81 - 34 = 65

65 degrees is congruent to x, so x is 65 degrees.

To find z, we can use the supplementary angles theorem.

x + z = 180

(65) + z = 180

z = 115 degrees.

Using the inner angles theorem (forgot what it was fully called), we see that the angles are congruent for z and for the angle next to 34 degrees, so we can say that the triangles are congruent using the side angle side theorem.

So, that means 6 is equal to y.