Explanation:
9. x and z are equal. y+z=90
148-x=180 x+148 are supplementary
-148 -148 Subtract 148 from both sides to isolate x
x=32 degrees
z=32 degrees b/c x and z are equal
y+z=90 y and z are complementary
y+(32)=90 Substitute 32 in for z
-32 -32
y =58 degrees
10. (4x-25)=(2x+7) B/c of the bisection, the two angles are equal.
4x-25 =2x+7 Remove parenthesis
-2x -2x Subtract 2x from both sides
2x-25 = +7
+25 +25 Add 25 to both sides to isolate x
2x = 32
/2 /2 Divide both sides by 2 to isolate x
x = 16
(4(16)-25)+(2(16)+7)=78 degrees Substitute 16 into the equation, this time adding the values instead of setting them equal to get the angle measure requested.
11. (6x-47)+(x+4)=90 Angles that are complementary add up to 90 degrees
7x-43 =90 Add like terms
+43 +43 Add 43 to both sides to isolate x
7x =133
/7 /7 Divide both sides by 7 to isolate x
x =19
((19)+4)=23 degrees Substitute x into the angle measure requested
12. 180=2x-9+x Use the words to help you determine what each value is.
180=3x-9 Add like terms
+9 +9 Add 9 to both sides to isolate x
189=3x
/3 /3 Divide both sides by 3 to isolate x
63=x
2(63)-9=177 degrees Substitute 63 into x to find the requested angle measure.