Question

KITES The kite shown is made of two congruent triangles. If m∠BAD=m∠BCD=45°
, find m∠ABD

Answer 1

Since the kite is made of two congruent triangles, we know that m∠BCD = m∠CBD. Since m∠BAD = 45°, we know that m∠ABC = 180° - m∠BAD = 180° - 45° = 135°. Therefore, m∠ABC + m∠CBD = 135° + m∠CBD = 180°. Solving for m∠CBD, we get m∠CBD = 45°. Since m∠ABD = m∠ABC - m∠CBD, we get m∠ABD = 135° - 45° = 90°. Therefore, m∠ABD = 90°.