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Based on the diagram, x=_____. Briefly explain your reasoning.

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novjb | Salutatorian

Posted July 10, 2013 at 12:27 AM via web

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Based on the diagram, x=_____. Briefly explain your reasoning.

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Tagged with angles, geometry, math, triangles

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llltkl | College Teacher | Valedictorian

Posted July 10, 2013 at 1:14 AM (Answer #1)

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Both the triangles shown in the image have one right angle each, which are congruent (because all right angles are congruent).

Again, both the triangles have one angle out of a pair of vertically opposite angles, which must be equal in measure.

Therefore, the two triangles are similar (AA postulate).

So, the remaining angle, in each case, must be equal in measure.

That means 2x=50

`rArr` x=25 degreees.

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