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For the figure shown, find m1 and m22. m21

Sagot :

Finding missing angles

We know that:

1. The sum of the inner angles of a triangles is 180º

2. Supplementary angles are the angles that together form a straight line, their addition is 180º

On the right triangle we have that

∡2 + 96º + 35º = 180º

∡2 + 131º = 180º

∡2 = 180º - 131º

∡2 = 49º

Since ∡1 and ∡3 are supplementary then

∡1 + ∡3 = 180º

∡1 + 49º = 180º

∡1 = 180º - 49º

∡1 = 131º

O the left triangle we have that

∡1 + ∡4 + 32º = 180º

131º + ∡4 + 32º = 180º

∡4 + 163º = 180º

∡4 = 180º - 163º

∡4 = 17º

Since ∡2 and ∡4 are supplementary then

∡2 + ∡4 = 180º

∡2 + 17º = 180º

∡2 = 180º - 17º

∡2 = 163º

Answer: ∡1 = 131º and ∡2 = 163º

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