Me guys pls ❤️❤️

determine the angle measure of the following angles ?

1) b =
2) m=
3) h=
4) g=
5) i=
6) j=

Answer

1)

2)

3)

4)

5)

6)

Explanation

From the diagram,

, corresponding angles are equal.

From the diagram, m=k, corresponding angles are equal.

But k+130=180, angles on a straight line sum up to 180 degrees.

This implies that k=180-130=50

From the diagram ; ,angles on a straight line sum up to 180 degrees.

From the diagram, vertically opposite angles are equal.

From the triangular portion;

i+h+m=180. sum of interior angles of a triangle.

This implies that:

i+79+50=180

i+129=180

i=180-129

Finally

, vertically opposite angles are equal.

Part 1) ∠b=101°

Part 2) ∠m=50°

Part 3) ∠h=79°

Part 4) ∠g=101°

Part 5) ∠i=51°

Part 6) ∠j=130°

Step-by-step explanation:

Part 1) ∠b

we know that

∠b=101° > by corresponding angles

Part 2) ∠m

we know that

∠m=∠k > by corresponding angles

and

∠k+130°=180° > by supplementary angles

∠k=180°-130°=50°

therefore

∠m=50°

Part 3) ∠h

we know that

∠h+101°=180° > by supplementary angles

∠h=180°-101°=79°

Part 4) ∠g

we know that

∠g=101° > by vertical angles

Part 5) ∠i

we know that

The sum of internal angles of a triangle must be equal to 180 degrees

so

∠h+∠m+∠i=180°

substitute the values and solve for ∠i

79°+50°+∠i=180°

∠i=180°-129°=51°

Part 6) ∠j

we know that

∠j=130° > by vertical angles

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