Answer:
m ∠ AMC = 75°
Step-by-step explanation:
Given:
In Δ ABC, m ∠C=90°
m∠ B =30°
CM is angle bisector
We need to find m ∠AMC
In Δ ABC Sum of all angle is 180° so we get,
[tex]m\angle A+m\angle B+m\angle C =180\\m\angle A+90+30 =180\\m\angle A+120 =180\\m\angle A=180-120\\m\angle A=60[/tex]
Now we know that CM is angle bisector of ∠C
∴ [tex]m\angle ACM +m\angle BCM =90\\m\angle ACM +m\angle ACM =90\\2m\angle ACM =90\\m\angle ACM =\frac{90}{2}=45[/tex]
Now in Δ ACM we know that Sum of all angles is 180
[tex]m\angle ACM + m\angle AMC + m\angle A=180\\45 + m\angle AMC + 60 =180\\105 + m\angle AMC =180\\m\angle AMC =180 -105 =75[/tex]
Hence m ∠ AMC = 75°
