Question

For the quadrilateral ABCD diagonal BD is an angle bisector for angles B and D. Find the m∠DAC if m∠ADB = 20°, m∠DBC = 60°.

Answer 1

m∠DAC = 70°

m∠ACB = 30°

Explanation:

Answer 2

70°

Explanation:

If in the quadrilateral ABCD diagonal BD is an angle bisector for angles B and D, then

• ∠ABD ≅ ∠DBC;
• ∠ADB ≅ ∠BDC.

Consider triangles ABD and CBD. In these triangles,

• ∠ABD ≅ ∠DBC;
• ∠ADB ≅ ∠BDC;
• BD ≅ BD.

Hence, triangles ABD and CBD are congruent by ASA postulate.

So, AD ≅ DC.

Now, consider triangle ADC. This is an isosceles triangle, because AD ≅ DC. In this triangle, m∠ADC = m∠ADB + m∠BDC = 20° + 20° = 40°. AC is the base. Angles DAC and DCA are congruent as adjacent angles to the base AC, so

m∠DAC = 1/2 (180° - 40°) = 70°