Question

82°

57°
The measure of x is
The measure of y is
The measure of z is
to
Z
102
62⁰

Answer 1

Answers:

x = 16

y = 41

z = 123

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Step-by-step explanation:

Focus on the large triangle on the left.

The three interior angles of any triangle add to 180 degrees.

57+82+y = 180

y+139 = 180

y = 180-139

y = 41

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Now focus on the large triangle on the right.

We'll use the same idea as before.

x+102+62 = 180

x+164 = 180

x = 180-164

x = 16

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The last triangle to focus on is the small one in the middle.

Use the values of x and y to find z.

x+y+z = 180

16+41+z = 180

57+z = 180

z = 180-57

z = 123

Answer 2

The angles inside of a triangle always add up to 360 therefore we can easily determine what the angle of x and y is because they are a part of two triangles that have two angles each. Let's first determine x.

`x = 180 - (102+ 62)`

`x = 180 - 164`

`x = 16`

The second step that we need to do is to determine y using 82 and 57.

`y = 180 - (82 + 57)`

`y = 180 - 139`

`y = 41`

The final step is to determine z using x and y

`z = 180 - (x + y)`

`z = 180 - (16 + 41)`

`z = 180 - 57`

`z = 123`

Therefore, x = 15 and y = 41 and z = 123

Hope this helps!