He heights of △abc are drawn from vertices a and c. these heights intersect at point m. find m∠amc, if m∠a=70° and m∠c=80°.

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°

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