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mote1985 [20]
2 years ago
8

Instructions: Find the angle measures given the figure is a rhombus. Please Help!

Mathematics
2 answers:
nataly862011 [7]2 years ago
7 0

Answer:

30

Step-by-step explanation:

since this is rhombus 1 2 3 4 must be equal

|NP|=|MN|

so 180-120=60

60/2=30

Alekssandra [29.7K]2 years ago
5 0

Answer: All four angles (angle1,2,3,4) are 30 degrees each

===========================================================

Explanation:

A rhombus has all four sides that are the same length. Think of a square, but we don't necessarily need to have all four angles be 90 degrees (as the diagram indicates).

Focus on triangle MNP. We have N = 120 degrees. We also know that MN = NP due to the fact all four sides of a rhombus are the same length.

This immediately leads to triangle MNP being isosceles. The base angles opposite the congruent sides are congruent angles. So angle 1 and angle 3 are the same measure. For triangle MNP, angle M and angle P are the same.

Let's find the missing angle

M+N+P = 180 ... angles of a triangle add to 180

M+120+M = 180 ... plug in N = 120, replace P with M

2M+120 = 180

2M = 180-120 ... subtracting 120 from both sides

2M = 60

M = 60/2 .... dividing both sides by 2

M = 30

So N is also 30 degrees

------------------------

We've found that both angle 1 and angle 3 are 30 degrees each.

Any rhombus is a parallelogram, which means that angles 1 and 4 are congruent alternate interior angles. Similarly, angles 2 and 3 are the other pair of alternate interior angles.

Therefore, we can say

angle 1 = angle 4 = 30 degrees

angle 2 = angle 3 = 30 degrees

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Andrew should make 6 bookcase and 12 tv stand to maximize his profut $1560.

Given that 18 pieces of furniture is made and the materials for each bookcase cost him $20.00 and the materials for each TV stand cost him $40.00 and he has $600.00 to spend on materials. He makes a profit of $60.00 on each bookcase and a profit of $100.00 for each TV stand.

Let x represent the number of book case and let y represent number of tv stand.

Total number of book case and total number of tv stand is x+y≤18     ......(1)

Total amount of book case and total amount of tv stand is 20x+40y≤600   ......(2)

minimum amount of book case is x≥0 and minimum amount of tv stand is y≥0.

Now, solve the inequality (1) by converting it into equality and substituting x=0 and y=0, we get

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When y=0 then

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Further, we will grph the inequalities and we get feasible region and taking boundary point from graph.

From the graph the vertices of the feasible region is (0,0),(6,12),(0,15) and (18,0)

Further, we will find the maximization profit for the equation Z=60x+100y

When (x,y)=(0,0) then

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When (x,y)=(0,15) then

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