SOLUTION: Find angle C, in degrees in the following Diagram: Please find my diagram here: https://drive.google.com/file/d/1BkVlpWbTavh-X4fBbyDESblXowg0eNii/view?usp=sharing Apperciate

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Find angle C, in degrees in the following Diagram: Please find my diagram here: https://drive.google.com/file/d/1BkVlpWbTavh-X4fBbyDESblXowg0eNii/view?usp=sharing Apperciate       Log On

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Question 1197065: Find angle C, in degrees in the following Diagram:
Please find my diagram here: https://drive.google.com/file/d/1BkVlpWbTavh-X4fBbyDESblXowg0eNii/view?usp=sharing
Apperciate it. Thanks.
Found 3 solutions by MathLover1, ikleyn, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
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Capture10-9-2022-4-22-57-PM

as you can see, there are three right angles
first find the measure of angle b
b=90-37=53°
then we know that the sum of 2b plus third angle in second right triangle is 180
third angle in second right triangle is 90-a°
so,
2b%2B%2890-a%29=180°
2%2A53%2B90-a=180°
196-180=a°
a=16°

since angle c in third right triangle is equal in measure to the third angle in second triangle which is 90-a, we have

c=90-16°
c=74°

Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

            The solution by @MathLover1 is  INCORRECT.

            It is incorrect,  because she starts from wrong assumption that  " there are three right angled triangles ".

            The problem  NOWHERE  says it:  this assumption is not supported by the problem,
            so it is only in her imagination:  it is not a given fact.

            So,  I came to bring a correct solution. 


Let A be the vertex at angle "a";
    B be the vertex at angle "b",
    C be the vertex at angle "c",
    D be the vertex at angle 37°,
    P be the intersection point of the two sloped lines.


From triangle ABC, we can write equation 

    angle(A) + angle(B)  + angle(C) = 180°

or

    2a       + (180°-2b) +    c     = 180°

or

    2a - 2b  + c =  0.     (1)



Next consider triangles APC and BPD.  From these triangles, we can write equation

    a + c = b + 37°.


It is because left  side (a+c) complements angle P to 180°,
same as       right side (b+37°) complements angle P to 180°.


Last equation is equivalent to

    a - b + c = 37°.       (2)


Thus we have two equations (1) and (2)

    2a - 2b  + c =  0.     (1)
    a  -  b  + c = 37°.    (2)


Multiply equation (2) by 2;  then subtract equation (1).  You will get

    c = 2*37° = 74°.


ANSWER.  The measure of angle "c" is 74°.

Solved  (correctly).



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Find angle C, in degrees in the following Diagram:
Please find my diagram here: https://drive.google.com/file/d/1BkVlpWbTavh-X4fBbyDESblXowg0eNii/view?usp=sharing
Apperciate it. Thanks. 
bo = a + 37o ----- External angle = sum of interior opposite angles
b + b = 2(a + 37)
2b = 2a + 74
2b = 2a + c ----- External angle = sum of interior opposite angles
Therefore, 2a + 74 = 2a + c
2a + 74 - 2a = c
74o = c