Answer:
Step-by-step explanation:
The are 180 degrees in a triangle and 180 degrees on a line. Therefore, call the third angle of the triangle 
.
The following equation solves for :
Solving for 
:
Answer:
x < 9
Step-by-step explanation:
Given inequality:
6x + 9 < 63
Subtract 9 from both sides:
⇒ 6x + 9 - 9 < 63 - 9
⇒ 6x < 54
Divide both sides by 6:
⇒ 6x ÷ 6 < 54 ÷ 6
⇒ x < 9
Answer:
∠1=135°
∠2=45°
∠3=45°
∠4=135°
∠5=135°
∠6=45°
∠7=45°
∠8=135°
Step-by-step explanation:
→∠1=∠4[Being vertically opposite angles]
→∠4=135°
→∠1=∠5[Corresponding angles]
→∠5=135°
→∠5=∠8[Being vertically opposite angles]
→∠8=135°
→∠1+∠2=180°[Sum of linear pair]
→∠2=180°-135°
→∠2=45°
→∠2=∠3[Being vertically opposite angles]
→∠3=45°
→∠3=∠6[Alternate angles]
→∠6=45°
→∠6=∠7[Being vertically opposite angles]
→∠7=45°
As we move from point Z to point Y, x increases by 8 and y increases by 3. Thus the length of line segment ZY is sqrt(8^2 + 3^2) = sqrt(73), by the Pythagorean Theorem. That's approx. 8.54.
You could also leave your answer in the form √(8^2 + 3^2).
When you have angle and its corresponding (opposite) side then you need to use law of sin. Problems 3,4,5(in 5 you need at first find angle X=180-92-62)
when you have two sides and angle between them, this is law of cos, problem 6,8
problem 7 you can use both, but if you can use both better to use law of sin, it is just easier
