Answer:
x = 70°
Step-by-step explanation:
The relevant relations are ...
- base angles of an isosceles triangle are congruent
- consecutive interior angles where parallel lines meet a transversal are supplementary
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Triangle OBQ is isosceles, so angle OQB = 40°. Triangle OPQ is isosceles, so angle OQP is x. The sum of angles OQB and OQP is angle BQP, which is supplementary to angle OPQ. That is, ...
(40° +x) +x = 180°
2x = 140° . . . . . . subtract 40°
x = 70° . . . . . . divide by 2
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There are many ways to find x. The one shown here is just one of them. In general, right triangles, isosceles triangles, symmetry, inscribed angles can all be used to write relations involving the known angles and x.
The value of x is all real numbers because 6^0 is 1 and 1 raised to the power of any number will still be 1.
This problem is already a bit more simple since they give you the amount of fabric per sock. Now, to solve, you will want to divide 9 3/4 by 5/6. However, if you don't have a calculator, it's rather inconvenient to solve with a fraction, so convert the fraction to a decimal, which should leave you as 9.75 divided by .83333333. Your final answer should be somewhere around 11.7 socks. Since you can't make 7/10 of a sock, your answer should be around 11 socks.
Answer:
X is right there
Step-by-step explanation:
See?
Let a = longest side <em> (Establishing labels)</em>
let b = shortest side
let c = third side
P = 14.5 <em> (Given)</em>
a = 6.2
b = 1/2(a)
P = a + b + c
P = 6.2 + 3.1 + c <em>(Fill in given info in equation)</em>
P = 9.3 + c <em>(Simplify)</em>
14.5 = 9.3 + c <em>(Simplify)</em>
c = 14.5 - 9.3 <em>(Solve)</em>
c = 5.2
Hope this made sense!
