Answer:
x=63°, y=47°, w=70°, z=121°
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 sum of all interior angles in a triangle is 180°
- The sum of all exterior angles in a triangle is 360°
- Two adjacent angles formed by the intersection of two lines add up to 180° (linear angles)
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°