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.
The sum of the interior angle measures of an n-sided polygon is (n-2)180^(∘).
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.
