Question

Determine the measure of angle A. PLEASE HELP PLEASE.

Answer 1

Answer: Choice C) 36 degrees

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Explanation:

Place point B at the intersection of the lines where the 90 degree angle is located.

Place point C at the other intersection point.

So we have triangle ABC.

Since we have a right angle, this means angle B is 90 degrees.

Angle C is 55x-1 degrees because it's vertical to the angle shown. Vertical angles are congruent.

See the diagram below.

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From here we use the idea that all three angles of any triangle always add to 180

A+B+C = 180

(36x) + (90) + (55x-1) = 180

91x+89 = 180

91x = 180-89

91x = 91

x = 91/91

x = 1

Use this x value to find angle A and C

A = 36x = 36*1 = 36

C = 55x-1 = 55*1-1 = 54

Finding angle C is optional since your teacher just wants angle A, but it's useful to help check our answer

A+B+C = 36+90+54 = 180

So this confirms we have the right x value.

Answer 2

First we find the value of $x$. This is quite simple as it's a right angled triangle with one of the angles already given. The main concept is vertically opposite angles meaning if 2 lines intersect, the opposite 2 angles are equal.

So the angle $55x - 1$ is for the interior of the triangle too. Now due to angle sum postulate, $36x + 55x -1 + 90 = 180$

Simplify this and you get: $91x = 91$

Hence, $x = 1$

Now, we need to find the value of angle $A$ which is $36x$ which is basically $36 * 1$ when we replace $x$ with $1$.

Henceforth, angle $A$ is equal to $36$ so option $C$ is correct. :D