Question

Please Help!!!!!! Use what you've learned today about the sum of the interior angles of triangles and quadrilaterals to determine the measure of ALL unknown angles in the figure below.​

Answer 1

m = 116

x = 24

y = 76

z = 40

Explanation:

For startes the interior angles of triangles always add up to 180 degrees.

That means....

73 + 83 + x = 180

z + m + x = 180

z + y + 64 = 180

Another important fact is that two angles that are intersected by a line in the case 64 and m always add up to 180 degrees.

So m + 64 = 180

Let's start with 73 + 83 + x = 180

If you add 73 and 83 you get 156

x + 156 = 180 then subtract 156 from both sides and

x = 24

Then use m + 64 = 180 subtract 64 from both sides and

m = 116

z + m + x = 180 become

z + 116 + 24 = 180

Add 116 and 24 and you get 140

z + 140 = 180 subtract 140 from both sides and

z = 40

Check to make sure m + x + z = 180

24 + 40 + 116 = 180

z + y + 64 = 180 becomes

y + 40 + 64 = 180

40 + 64 = 104 so

y + 104 = 180 subtract 104 from both sides and

y = 76

Congratulations you have found all of the angles!