Answer: 150°
Step-by-step explanation:
In the given triangle ABC ∠A=70°, ∠C=80°
therefore ∠B=180-(∠A+∠C)=180-(70+80) [sum angle property of triangle]
⇒∠B=30°
Now, heights(altitude) are drawn from vertices A and C on respective bases
they intersect at a point M. Also, we know that heights are perpendicular on the bases.
Also, point of intersection of altitudes is called orthocenter.
Now since M is orthocenter, ∠ABC+∠AMC=180° (property of orthocenter in a triangle)
⇒30°+∠AMC=180°
⇒∠AMC=180°-30°=150°
Hence in the triangle ABC, ∠AMC=150°
