Q4 of 24 Page 15

In the figure below, M is the midpoint of the line AB. Compute the other two angles of ∆ABC.

Given, M is the midpoint of the line AB and ∠m = 90⁰.

∠a = 50


We know sum of all interior angles of a triangle is 180⁰.


In ∆AMC,


∠a + ∠b + ∠c = 180⁰


50⁰ + 90 + ∠c = 180⁰


140⁰ + ∠c = 180⁰


∠c = 180⁰-140⁰


∠c = 40⁰


In ∆MBC,


∠c = 40⁰


∠m = 90⁰


∠b = ?


∠m + ∠b + ∠c = 180⁰


90⁰ + ∠b + 40⁰ = 180⁰


130⁰ + ∠b = 180⁰


∠b = 180⁰-130⁰


∠b = 50⁰



∠a = 50⁰, ∠b = 50⁰, ∠c = 80⁰


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