Answer:
Karen needs to spend $4.5 to buy new hair bands.
Step-by-step explanation:
Given:
Hair bands Karen have = 3
cost of 8 hair bands = $1
Total Hair bands she require = 39
Hence Number of of new hair bands require = Total Hair bands she require - Hair bands Karen have = 39 -3 = 36
we need to find how much money she need to spend to buy new hair bands.
cost of 8 hair bands = $1
Cost of 36 hair bands = money need to spend on hair bands
By using Unitary method we get;
Money spend on new hair bands = 
Hence,Karen needs to spend $4.5 to buy new hair bands.
The angle relationship and their reasons are:
- m∠HED = m∠FEJ ---> Vertical angles theorem
- m∠KFE = m∠DEH ---> Alternate interior angles theorem
- m∠LFG = m∠DEH ---> Alternate exterior angles theorem
- m∠JEF + m∠LFE = 180° ---> same-side interior angles theorem
- m∠DEJ = m∠EFL ---> Corresponding interior angles theorem
- m∠LFG + m∠GFK = 180 ---> linear pair
The angle pairs are formed based on their relative positions. The following shows each angle relationship and their reasons:
∠HED and ∠FEJ are directly vertically opposite each other, therefore, they are equal based on the vertical angles theorem.
- m∠HED = m∠FEJ ---> Vertical angles theorem
∠KFE and ∠FEJ are alternate interior angles, therefore, they are equal based on the alternate interior angles theorem.
- m∠KFE = m∠DEH ---> Alternate interior angles theorem
∠LFG and ∠FEJ are alternate exterior angles, therefore, they are equal based on the alternate exterior angles theorem.
- m∠LFG = m∠DEH ---> Alternate exterior angles theorem
∠JEF and ∠LFE are interior angles on same side of the transversal, therefore, the sum of both angles equal 180 degrees based on the same-side interior angles theorem.
- m∠JEF + m∠LFE = 180° ---> same-side interior angles theorem
∠DEJ and ∠EFL are corresponding angles, therefore, they are equal based on the corresponding angles theorem.
- m∠DEJ = m∠EFL ---> Corresponding interior angles theorem
∠LFG and ∠GFK are angles on a straight line, therefore the sum of both angles will equal 180 degrees because they are a linear pair.
- m∠LFG + m∠GFK = 180 ---> linear pair
Learn more about angle relationship on:
brainly.com/question/12591450
Answer:
x= -4
Step-by-step explanation:
∠LMP + ∠PMN= 180° (adj. ∠s on a str. line)
-16x +13 -20x +23= 180
bring x term to 1 side, constant to the other:
-36x= 180 -13 -23
Simplify:
-36x= 144
x= 144 ÷ (-36)
x= -4
*The sum of the angles on a straight line is 180°
