Find the value in f each variable

x=63°, y=47°, w=70°, z=121°

Step-by-step explanation:

Angles in a Triangle

To find the value of the variables given in the figure, we must recall some properties of the angles in a triangle and in a line:

The exterior angles of the triangle have the measures z-13, z, and z+10. They must add up to 360°, thus:

z - 13 + z + z + 10 = 360

Simplifying:

3z - 3 = 360

Adding 3:

3z = 360 + 3 = 363

z = 363/3

z = 121°

Now we use the bottom left vertex of the triangle, where the angles z-13 and w must add up to 180° because they are linear angles:

z - 13 + w = 180

Since z=123°

123 - 13 + w = 180

Rearranging:

w = 180 - 123 + 13

w = 70°

Similarly angles y and z+10 are linear, thus

y + z + 10 = 180

y + 123 + 10 = 180

Solving:

y = 47°

Finally, the sum of the interior angles of the triangle is 180°, thus:

x + 70 + 47 = 180

x = 180 - 70 - 47

x = 63°

Solution: x=63°, y=47°, w=70°, z=121°

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step-by-step explanation:

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