a. I and II only true statement.
b . ∠3 = 84°
c . m∠KJM = 138° and m∠KLM = 59°
Properties of an Isosceles trapezium
- Only one pair of sides are parallel
- The diagonals are equal in measure.
- The opposite angles are supplementary
- The base angles are equal in measure.
Therefore, i and ii are true for an isosceles trapezium.
∠2 ≅ ∠3
∠1 ≅ 96°
Therefore,
∠3 = 180 - 96
∠3 = 84°
m∠KJM = 180 - x - 14
5x - 2 = 180 - x - 14
5x - 2 = 180 - x - 14
5x + x = 180 - 14 + 2
6x = 168
x = 168 /6
x = 28
m∠KJM = 5(28) - 2 = 138°
m∠KLM = 180 - 10y + 29
3y + 14 = 180 - 10y + 29
3y + 10y = 180 + 29 - 14
13y = 195
y = 195 / 13
y = 15
m∠KLM = 3(15) + 14
m∠KLM = 45 + 14
m∠KLM = 59°
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