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Angle Sum Theorem what is y

Angle Sum Theorem what is y-example-1
User Sloane
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1 Answer

19 votes
19 votes

9514 1404 393

Answer:

y = 90°

Explanation:

The angle sum theorem tells you the sum of angles in a triangle is 180°. You also know that the sum of the angles of a linear pair is 180°.

Let z represent the measure of the unmarked interior angle at the the lower left of the triangle shown. Then we have ...

110° + z = 180° . . . . angles of a linear pair are supplementary

z +2x +70° = 180° . . . Angle Sum theorem

Then we can write ...

110° +z = z +2x +70°

110° = 2x +70° . . . . . the exterior angle is equal to the sum of the remote interior angles.

40° = 2x . . . . . . . . . subtract 70°

20° = x

Similarly, we have ...

110° = x + y . . . . . . . exterior angle = sum of remote interior angles

110° -20° = y = 90° . . . . subtract x=20°

_____

Additional comment

You may be able to get there a lot faster by recognizing z = 180° -110° = 70°, hence the triangle is isosceles. The angle bisector creating angles x is then also an altitude, hence y = 90°.

User Sayuri Mizuguchi
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3.3k points