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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°

_____

<em>Additional comment</em>

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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Can someone please find the volume of this shape and show work for how you did it??

castortr0y [4]

Answer:

$221.4m^{3}$

Step-by-step explanation:

To work out the volume of this shape you will first need to work out the area of the triangle. To work out the area of the triangle you would multiply the base of 12 by the height of 4.1, which gives you 49.2. You would then need to divide 49.2 by 2, which gives you 24.6. This is because the formula for the area of a triangle is the same as that of a square, however a triangle is half of a square with the same length and width. To work out the volume you would multiply the area of the triangle, which is 24.6 by the height of 9, which gives you 221.4 $m^{3}$