Solve for w solve for x solve for y

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

w = 58°

x = 32°

y = 16°

Step-by-step explanation:

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12