Remember that all the diagonals in a rectangle are congruent and bisect each other.
x=6
y=-10
Practice makes perfect
We are given some measures of angles in a rectangle ABCD in terms of x- and y-terms, and we are asked to find the values of x and y. Let's start with graphing this rectangle and highlighting the given angles.
We know that all four angles in a rectangle are right angles. This means that the sum of m∠ABE and m∠EBC is equal to 90. Let's use this information to find the value of x.
These angles have measures of 30. Next let's notice that ∠DEC and ∠AEB are vertical angles, so they have the same measure. Therefore, we can write that m∠AEB is also 10-11y.
To find the value of y, we can use the Triangle Sum Theorem. Recall that, according to this theorem, the sum of the measures of angles in a triangle is always 180. Let's substitute 30 for m∠EAB and m∠ABE, and 10-11y for m∠AEB.
