will you please help answer angle questions using a shape X. Shape X ........ #2 is in the top space of the x, #3 is in the right space of the x, #4 is in the bottom space of the x, and #1 is in...

will you please help answer angle questions using a shape X.

Shape X ........ #2 is in the top space of the x, #3 is in the right space of the x, #4 is in the bottom space of the x,

and #1 is in the left space of the x.

1.  solve  m`/_` 3 + m`/_` 4 = ??

2.  if m`/_` 1 =(4x + 12) degrees, m`/_` 2 = (7x +3)degrees, and m`/_`  3 = 6y degrees

      then x = _____, m`/_` 1 = ______m`/_` 2=______ and y =_____________

thanks

Asked on by marley112

3 Answers | Add Yours

gsenviro's profile pic

gsenviro | College Teacher | (Level 1) Educator Emeritus

Posted on

to solve for y, you can use either of the following:

1) m<2 + m<3 = 180  and substitute values of <2 and <3 in terms of x and y and also substitute the value of x as obtained earlier.   OR

2) m<1 = m<3 and use this to solve for y.

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gsenviro | College Teacher | (Level 1) Educator Emeritus

Posted on

In the given question, Shape X has been divided into 4 quadrants, starting with #1 on left side and going clockwise from there.

To solve the question, remember angles on a straight line always add up to 180 degrees.

Thus, 1) m<3 + m<4 = 180 degrees

2) m<1 + m<2 = 180 = 4x+12 + 7x+3 = 11x + 15 => 11 x = 180-15 =165 => x = 165/11 = 15

Thus, x = 15 degrees; m<1 = 4x15 + 12 = 72 degrees, m< 2 = 7x15+3 = 108 degrees.

and using m<1 = m<3 = 72 (corresponding angles); similarly, m<2 =m<4 = 108 degrees

6 y =72 => y = 12 degrees

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