Question

(Angles in

The figure shows a parallelogram ABCD where BÂD = 64°
Elies on AB such that AÐE = 49°.
C С
D
49
Calculate
(i) ABC,
(ii) CỘE.
64
B
A
E​

Answer 1

m<ABC = 116°

m<CDE = 67°

Explanation:

✔️m<ABC = 180 - m<BAD (adjacent angles of a parallelogram are supplementary)

m<ABC = 180 - 64° (Substitution)

m<ABC = 116°

✔️m<CDA = m<CDE + m<ADE (angle addition postulate)

m<CDA = m<CDE + 49°

m<CDA = m<ABC (opposite angles of a parallelogram are congruent)

m<CDE + 49° = 116° (substitution)

m<CDE = 116° - 49° (Substraction property of equality)

m<CDE = 67°