Let's find the value of each angle and the value of x in the given isosceles trapezoid one at a time.
Angle Measures
Recall that if a quadrilateral is an isosceles trapezoid, then each pair of base angles is congruent. Therefore, ∠1 and the 62^(∘) angle are congruent. This means that their measures are equal.
m ∠1 = 62By the same fact, we know that the measures of ∠2 and ∠3 are equal.
m ∠2 = m ∠3
Next, because the bases of trapezoids are parallel, we can say that the 62^(∘) angle and ∠2 are same-side interior angles. Angles that form same-side interior angles along one leg are supplementary. This means that they add up to 180.
62+m ∠2 = 180 ⇔ m ∠2 = 118
We already know that m ∠2=m ∠3, so m ∠3 is also equal to 118. Let's add the measures of these angles to our diagram.
Value of x
Because we know that the given figure is an isosceles trapezoid, we know that its legs are congruent. Therefore, the lengths of the legs are equal.
x+2=5x-8
Let's solve this equation to find the value of x!
To find the side lengths, we can substitute x= 52 into either of the given expressions.
ccccc
x+2 & ⇒ & 5/2+2 & = & 9/2 [0.8em]
5 x-8 & ⇒ & 5( 5/2)-8 & = & 9/2
Now we can complete our diagram.
