Question

AB ll CD and EF ll GH use the figure above to find the value of each angle

Answer 1

Answer:

Part 1) ∠n=63°

Part 2) ∠m=117°

Part 3) ∠k=117°

Part 4) ∠x=117°

Part 5) ∠w=117°

Step-by-step explanation:

Part 1

Find the measure of angle n

we know that

∠n=63° ----> by alternate exterior angles

Part 2

Find the measure of angle m

we know that

∠n+∠m=180° ----> by supplementary angles

we have

∠n=63°

substitute

63°+∠m=180°

∠m=180°-63°=117°

Part 3

Find the measure of angle k

we know that

∠k=∠m ------> by vertical angles

we have

∠m=117°

therefore

∠k=117°

Part 4

Find the measure of angle x

we know that

∠x=∠k ------> by corresponding angles

we have

∠k=117°

therefore

∠x=117°

Part 5

Find the measure of angle w

we know that

∠w=∠x ------> by alternate interior angles

we have

∠x=117°

therefore

∠w=117°

Answer 2

Answer:

$x=k=117\°$

Step-by-step explanation:

Givens

AB || CD

EF || GH

These parallels gives us certain pair of angles which are congruent.

The given angle 63° is congruent with its corresponding angles. The image attached shows all corresponding angles that are equal to 63° (red angles).

Basically,

$x+63=180$ and $k+63=180$, by suplementary angles and straight angle definition.

Then, solving for $x$ and $k$, we have

$x=180-63\\x=117\°$

$k=180-63\\k=117\°$

Therefore, both angles are equal to 117°.