Exercise 50 Page 528

We want to find the measure of ∠ ZYX in our kite. In a kite, exactly one pair of opposite angles are congruent. In our kite, these angles are ∠ ZWX and ∠ ZYX. Since m∠ ZWX= 13x+14 it must also be that m∠ ZYX= 13x+14. Let's add these angle measures along with the rest of the angles that have been given.

Recall the Polygon Interior Angles Sum Theorem

By substituting n= 4 into the formula, we can determine the sum of the kite's interior angles. ( 4-2)180^(∘)=360^(∘) When we know the sum of the kite's interior angles, we can set the sum of the angle's equal to this number. 35^(∘)+( 13x+14)^(∘)+( 13x+14)^(∘)+( 13x+24)^(∘) = 360^(∘) Let's solve this equation to find x.

Finally, we will substitute x^(∘)= 7^(∘) into the expression for m∠ ZYX to find its measure. m∠ ZYX=13( 7^(∘))+14=105^(∘)