Answer/Step-by-step explanation:
The angles where two unequal sides of a kite meet are congruent to each other. Thus, these two opposite angles in a kite are equal to each other.
Therefore:
7. <E = <G
Sum of interior angles of a quadrilateral = 360
Thus,
<E = (360 - (150 + 90))/2
<E = 120/2
<E = 60°
<E = <G (set of congruent opposite angles of a kite)
Therefore,
<G = 60°
8. <H = <F (set of congruent opposite angles of a kite)
<F = right angle = 90°
Therefore:
<H = 90°
<G = 360 - (90 + 110 + 90) (sum of quadrilateral)
<G = 70°
9. Based on trapezoid midsegment theorem, the equation should be:
MN = (AB + DC)/2
Thus:
8 = (14 + DC)/2
8 * 2 = 14 + DC
16 = 14 + DC
16 - 14 = DC
2 = DC
DC = 2
10. A kite has only one set of opposite angles that are congruent to each other. The angles where the unequal sides meet, <B and <D, is the only set of angles that are congruent.
Therefore, m<A ≠ 50°
Rather, m<B = m<D = 120°
m<A = 360 - (120 + 120 + 50) (sum of quadrilateral)
m<A = 70°
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