Presumably l and m are parallel, so n and p are transversals across parallel lines. They'll make the obvious congruent angles and supplementary angles (add to 180 degrees) that presumably the questions will be asking about.
1. Angle 11 and angle 16. They're what's called vertical angles from a pair of crossing lines. Vertical angles are congruent, so m∠16 = 113°
2. Angle 1 and 3. Those are corresponding angles on a traversal of parallels, also congruent. m∠3 = 78°. You got this one right, good.
3. 7 & 8. They're what's called a linear pair, so are supplemental. 180-129=51 so m∠8 = 51°. You probably just subtracted wrong on this one.
4. 10 & 11. I forgot what these are called; interior angles or some such. Anyway they're supplementary so 180-77=103. m∠11 = 103°
5. 13 & 12. I forgot the name here too but they're congruent so m∠12 = 59°
6. 2 & 7. Again congruent so m∠7 = 130°
7. I don't know why they insist on making geometry into algebra. Here we have angles 1 & 8, which are congruent, so
5x + 2 = 3x + 28
5x - 4x = 28 - 2
2x = 26
x = 13
Answer:
∠B
Step-by-step explanation:
To convert from radians to degrees, multiply the radians by 180°/π
⇒ ∠B = 4 × 180°/π
⇒ ∠B = 229.2° (nearest tenth)
As 229.2° > 210° then ∠B is bigger than ∠A
Answer:
or 
Step-by-step explanation:
We use casework on when 
and when 
.
For the first case, , we add 9 to both sides to get
.
Dividing both sides by 3 gives
For the second case, , we add 9 to both sides to get
.
Dividing both sides by 3 gives
.
Checking both cases, we plug in 
and .
For the first case, we have 
, which satisfies the equation.
For the second case, we have 
, which also satisfies the equation.
This gives us two solutions to the equation; and .
Answer:
2
Step-by-step explanation:
