Answer:
w = 58°
x = 32°
y = 16°
Step-by-step explanation:
The triangle on the bottom is an isosceles triangle. They have two equal sides, which we know because two of the sides have a little tick through them.
All isosceles triangles have two equal angles that are not angle contained by the equal sides.
All triangles' interior angles add to 180°.
Using properties of triangles and isosceles triangles, we can find w.
64° + 2w = 180°
2w = 116°
w = 58°
The angle opposite to w is also 58°.
About that right angle, represented by a square: all right angles are 90°. This property is called complementary angles, meaning angles that add to 90°.
That angle is made of 58° + x.
58° + x = 90°
x = 32°
For the triangle on the left, it has an angle that connects to the 64°. Because it forms a straight line with the other angle, it adds to 180°. This property is called supplementary angles. That angle + 64° is 180°.
I will label it "a".
a + 64° = 180°
a = 116°
To find angle 2y, use the property where a triangles' angles add to 180°.
a + x + 2y = 180°
We already know "a" and "x", so we can substitute those values.
116° + 32° + 2y = 180°
2y = 32°
y = 16°
Summary of properties used:
All triangles' interior angles add to 180°
Isosceles triangles have two equal sides and two equal angles
Right angles add to 90°, called complementary angles
Straight lines add to 180°, called supplementary angles
