Mathematics
Grade9
Easy
Question
If ABCD is an isosceles trapezoid, the measure of ∠EBC is _____.
- 42°
- 38°
- 13°
- 180°
Hint:
An isosceles trapezoid can be defined as a trapezoid in which non-parallel sides and base angles are of the same measure. In other words, if two opposite sides (bases) of the trapezoid are parallel, and the two non-parallel sides are of equal lengths, then it is an isosceles trapezoid.
PROPERTIES :
1. One pair of sides is parallel and they are the base sides.
2. The remaining sides other than the base are non-parallel and are equal in length.
3. The base angles are the same.
4. The sum of opposite angles is 180° or supplementary.
The correct answer is: 38°
PROPERTIES of isosceles trapezoid :
1. One pair of sides is parallel and they are the base sides.
2. The remaining sides other than the base are non-parallel and are equal in length.
3. The base angles are the same.
4. The sum of opposite angles is 180° or supplementary.
∠ADC = ∠BCD = 71° ( The base angles of an isosceles trapezoid are equal.)
Since AD∥BE, ∠ADE and ∠BEC are corresponding angles.
The corresponding angles are equal.
So, ∠BEC = 71°
Now, in ΔEBC, ∠EBC = 180° - ∠BCE - ∠CEB
∠EBC = 38°
Thus, the measure of ∠EBC is 38°.
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