Question

The figure shows a rhombus ABCD. The diagonal DB is produced to E such that BC = BE and CDE = 46°.

Find
(I) BAD
(ii) BCE​

Answer 1

(i) 88°

(ii) 23°

Explanation:

See the picture below.

The numbers added in red are the angle measures. The numbers added in black are the order in which each angle measure was written.

ABCD is a rhombus, so all sides are congruent.

Triangle BCD is isosceles with sides DC and BC congruent, so <DBC is congruent to <BDC. From the sum of the measures of the angles of a triangle, we get m<DCB. Opposite angles of a rhombus are congruent, so m<A = m<DCB. From the sum of the measures of the angles of a triangle and from isosceles triangle ADB we get m<ADB and m<ABD. From m<DBC and supplementary angles, we get m<CBE. From isosceles triangle BCE, we get m<BCE.