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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

6. Trapezoids and Kites

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Exercise 8 Page 526

If a quadrilateral is an isosceles trapezoid, then opposite angles are supplementary.

100^(∘)

Practice makes perfect

Let's find the measure of ∠ K in JKLM.

In the quadrilateral, one pair of sides are parallel and the other pair are congruent. Therefore, this is an isosceles trapezoid. Recall that in an isosceles trapezoid, opposite angles are supplementary. This means the sum of m∠ M and m∠ K equals 180^(∘). m∠ M + m∠ K =180^(∘) By substituting m∠ M with its measure in this equation, we can solve for m∠ K by performing inverse operations.

m∠ M + m∠ K =180^(∘)

m∠ M= 80^(∘)

80^(∘)+m∠ K=180^(∘)

LHS-80^(∘)=RHS-80^(∘)

m∠ K=100^(∘)

Subchapter links

Exercises p.526-530