Answer:
27 degrees
Step-by-step explanation:
The easy way is by remembering the formula (a-b)/2=c, where a is the larger angle, and b is the smallest angle. (90-36)/2=27.
The longer, more drawn out answer goes as follows. See the image to understand the notation I use:
- AOE + BOD + BOA + DOE = 360
- AOE + BOD = 90 + 36 = 126
- BOA + DOE = 360 - AOE - BOD = 234
- Since the sum of a triangle's angles is 180, ODE = (180 - DOE) / 2
- Likewise, OBA = (180 - BOA) / 2
- Since CDE is 180, CDO = 180 - ODE = 180 - (180 - DOE) / 2
- Likewise, CBA is 180, so CBO = 180 - OBA = 180 - (180 - BOA) / 2
- The interior angles of the irregular polygon CBOD add up to 360, so CBO + CDO + BOD + BCD = 360.
- Substituting what we already found, 180 - (180 - BOA)/2 + 180 - (180 - DOE)/2 + 36 + BCD = 360
- Cleaning it all up, we get 180 + (BOA + DOE)/2 + 36 + BCD = 360
- As we found in line 3, BOA + DOE = 234, so substituting that in, 180 + 117 + 36 + BCD = 360
- Finally, solving for BCD (360 - 36 - 117 - 180) we get our answer, 27
Note: The long drawn out method shown above is a way to derive the formula for the secant theorem. You do not need to use this method every time. Just remember, large angle minus small angle, all divided by 2. That is it.
I will solve you system by substitution
y = 2x - 3 ; x + y = 1
→Step 1: Solve y = 2x - 3 for y
→Step 2: Substitute 2x - 3 for y in x + y = 1:
x + y = 1
x + 2x- 3 = 1
3x - 3 = 1 (Simplify both sides of the equation)
3x - 3 + 3 = 1 + 3 (Add 3 both sides)
3x = 4
3x ÷ 3 = 4 ÷ 3 (Divide each side by 3)
x = 4/3
→Step 3: Substitute 4/3 for x in y = 2x - 3:
y = 2x - 3
y = 2 (4/3) -3
y = -1/3 (Simplify both sides of the equation)
Answer:
x = 4/3 and y = -1/3
∫Hope that helps∫
You would need to cross multiply. When you do that you get x^2-7x-8x+56. Once simplifying you get x^2-15x+56.
Answer:
Step-by-step explanation:
Standard form: Ax+By=C
Change C to 53
Ax+By=53
He could have added a combination of $1 bills and $5 bills or just $1 bills.
I hope this is right