Answer:
#7) x = 5
∠VUJ = 82
∠JUT = 93
#8) x = 0
∠BJK = 146
∠IJB = 26
Step-by-step explanation:
#7) First off, let's find x. We know that the angle ∠VUT is made up of two angles, which is ∠VUJ and ∠JUT. In other words, if you add both these angles, it should equal ∠VUT. So something like this...
∠VUJ + ∠JUT = ∠VUT
Awesome, let's write this out. Remember that ∠VUJ equals 17x - 3? And ∠JUT equals 17x + 8? And ∠VUT equals 175°? The equation should now look like this...
17x - 3 + 17x + 8 = 175
Solve by combining like terms!
17x - 3 + 17x + 8 = 175
34x + 5 = 175
34x = 170
x = 5
Now that we know what x is, plug in 5 for x in the equations! So,
∠VUJ = 17x - 3 ∠JUT = 17x + 8
∠VUJ = 17(5) - 3 ∠JUT = 17(5) + 8
∠VUJ = 82 ∠JUT = 93
#8) This problem is exactly the same as #7.
Find x.
∠IJB + ∠BJK = ∠IJK
2x + 26 + 146 + 2x = 172
4x + 172 = 172
4x = 0
x = 0
Now that we know x, plug 0 in for x in the equations to solve and find the angles
∠IJB = 2x + 26 ∠BJK = 146 + 2x
∠IJB = 2(0) + 26 ∠BJK = 146 + 2(0)
∠IJB = 26 ∠BJK = 146
