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Find the range of values for $z$

(FIGURE CANNOT COPY)

$$-3.5<z<32.5$$

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Numerade Educator

University of Nottingham

Boston College

Utica College

to solve this problem. We will be using the converse of the hinge there. Um, which states, if you have your corresponding and congruent sides. So we've got this side on the left on the side on the right are marked congruent. We also know that we've got a shared side that is congratulated. But we also know the included angle between our corresponding congruent sides and because of the sides opposite of are included, angles are not congruent the converse of Hinge. Therm says the angles are not congruent. The angle opposite of the largest side is your largest angle. So by the Conn versus Hinge here, um, we know that the angles 72 degrees must be greater than to Z minus seven. Using some algebra I get 79 is greater than to Z and dividing by two we get Z is less than 79 over to, or we could say Z is less than 39.5. However, this is not the only condition we need to consider going back to Z being a variable inside an unknown angle measure. What we do know is that angle measured cannot equal zero. It's gotta be greater than zero, so we have to. Z minus seven is an angle measure and that must be greater than zero. If I add seven to both signs, I get to Z is greater than seven and dividing by two I get Z is greater than seven halves, or Z is greater than 3.5. So to find our range of Z, we will use all values of Z such that 3.5 is less than any Z value. But Z is also less than 39.5.