Respuesta :

gcantiga44

Answer:

y = 97

Step-by-step explanation:

Solve for z first.

Consider the biggest triangle's angles: z, 42°, and 55°

Total angle adds up to measure is 180°.

z + 42 + 55 = 180

z + 97 = 180

z = 180 - 97

z = 83°

Now consider the line angle: y and z

A line has an angle of 180°.

y and z are considered supplementary angles (angles that add up to 180°).

z = 83°

So,

y + z = 180

y + 83 = 180

y = 180 - 83

y = 97

First we will use both triangles to make one to find what x is for example:

angle 1: 42

angle 2: 55 + 26 = 81

angle 3: x = 180 - (angle 1 + angle 2) = 180 - 123 = 57

Now that we know what x is we can find what y is for example:

angle 1: 26

angle 2: x = 57

angle 3: y = 180 - (26 + 57) = 180 - 83 = 97

Now that we know what y is we can find what z equals knowing they are on a straight line which means that they both equal 180 degrees when they add up for example:

z = 180 - 97 = 83

Now that we know all of our variables we can check it by adding up the angles of the 3 triangles for example:

triangle 1: 81 + 42 + 57 = 180

triangle 2: 26 + 57 + 97 = 180

triangle 3: 55 + 42 + 83 = 180

So z = 83 and y = 97 and x = 57, Hope this helps a lot ^^

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