Question

Determine the measure of angle A. PLEASE HELP PLEASE.

a.54 DEGREES
b.1 DEGREES
c.36 DEGREES
d.32 DEGREES

Answer 1

Answer: Choice C) 36 degrees

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

Step-by-step 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.

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

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