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2 years ago

Angle Sum Theorem what is y

Mathematics

2 answers:

Mamont248 [21]2 years ago

6 0

9514 1404 393

Answer:

y = 90°

Step-by-step 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°.

zaharov [31]2 years ago

5 0

Answer:

y = 90°

Step-by-step 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°. are supplementary angles of a linear pair

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

40° = 2x.

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°.

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