3. Using the diagram below, fi nd each of the following angles and give the axiom or theorem used in each part to justify your answer. (i)
(ii) A F 65° D E B C
|∠A| |∠B|
(iii) |∠C| (iv) |∠D| (v)
|∠E| (vi) |∠F|
6. |∠EFC| in the diagram below is equal to 78 ° E A C D B
Find each of the following angles and give the axiom or theorem used in each part to justify your answer.
( i ) ( i i )
4. |∠UTR| in the diagram below is equal to 122 ° . Using the diagram, fi nd each of the following angles and give the axiom or theorem used in each part to justify your answer.
U R X Y V W
5. For each of the diagrams below, state whether each of the pairs of lines cut by the transversal are parallel or not, and give the axiom or theorem to justify your answer.
(i) 55° 55° 64°
Using the diagram, fi nd the following angles. (i)
|∠A| (ii) |∠B| (iii) |∠C|
9. Below is a map of a part of the city of Chicago, Illinois, USA. The angle between N Keeler Ave and W Grand Ave (marked as angle C in the map) is 68 ° . N Tripp Ave, N Keeler Ave, N Kedvale Ave are all parallel to each other.
Find the measure of the following angles. ( i )
|∠E| ( i i ) |∠B|
( i i i ) |∠A| ( i v ) | ∠D |
(ii) 65° T S (i) (ii) (iii)
|∠UTV| |∠TVW| |∠STV|
(iv) |∠WVY| (v)
|∠XVY|
|∠FCD| |∠GFH|
( i i i ) |∠ACF| ( i v ) |∠ACB|
7. Using the diagram shown, fi nd the measure of the following angles.
G
A 114° B
E F ( i ) ( i i )
|∠A| |∠E|
( i i i ) |∠C|
8. The diagram below shows a cross-section through a set of stairs.