Can anyone help me? I need an exact answer, please no guesses. Thanks in advance
2 answers:
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Option 3:
m∠ABC = 66°
Solution:
Given and ABH is a transversal line.
m∠FAB = 48° and m∠ECB = 18°
m∠ECB = m∠HCB = 18°
<u>Property of parallel lines: </u>
<em>If two parallel lines cut by a transversal, then the alternate interior angles are equal.</em>
m∠FAB = m∠BHC
48° = m∠BHC
m∠BHC = 48°
<u>Exterior angle of a triangle theorem: </u>
<em>An exterior angle of a triangle is equal to the sum of the opposite interior angles.</em>
m∠ABC = m∠BHC + m∠HCB
m∠ABC = 48° + 18°
m∠ABC = 66°
Option 3 is the correct answer.
Answer:
The number of pennies,nickels and dimes are (p,n,d)=(3,4,6).
Further explanation:
Given:
A box holding pennies, nickels and dimes contains thirteen coins in a box.
Total value is 83 cents.
Calculation:
Consider p,n and d be the number of pennies, nickel and dimes.
Now, total is 13 coins so
As we know that these following are US coin.
Penny=1 cent
Nickel=5 cents
Dime=10 cents
Step 1:
The value is already given as 83 cents that is 80+3 cents.
80 cents can be possible in many combinations as follows:
(N,D)=(0,8),(2,7),(4,6),(6,5),(8,4),(10,3),(12,2),(14,1),(16,0)
It is given that the total number of cents is 13 so we choose (4,6) as (n,d) .
So the value of nickel n=4
Dimes d=6
Step 2:
The value of p is calculated as follows:
Substitute 4 for n, 6 for d in equation as follows:
p=3
Thus, the number of pennies,nickels and dimes are (p,n,d)=(3,4,6).