In Δ ABC ∠ B = ∠ C and ray AX bisects the exterior angle ∠ DAC. If ∠ DAX =70°, then ∠ ACB =

Question

In &#x394; ABC &#x2220; B = &#x2220; C and ray AX bisects the exterior angle &#x2220; DAC. If &#x2220; DAX =70&#xB0;, then &#x2220; ACB =

Philoid · Accepted Answer

AX bisects ∠DAC

∠CAD = 2 * ∠DAC

∠CAD = 2 * 70^o

= 140^o

By exterior angle theorem,

∠CAD = ∠B + ∠C

140^o = ∠C + ∠C (Therefore, ∠B = ∠C)

140^o = 2∠C

∠C = 70^o

Therefore, ∠C = ∠ACB = 70^o