? asked in Science & MathematicsMathematics · 10 years ago

Parallelogram ACFD is split in two parts so that ABED and FEBC are congruent isosceles trapezoids.?

What are the measures of all the angles of trapezoid FEBC if angle D is 46°?

Angle C=

Angle F=

Angle <CBE=

Angle <FEB=

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  • 10 years ago
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    I assume you have a picture of this. If not, please draw one. Then you would see that

    angle DEB = angle D = 46 because ABED is an isosceles trapezoid

    angle FEB = (180 - angleDEB) = 134 because these are supplementary angles

    angle F = angle FEB = 134 because FEBC is an isosceles trapezoid

    angle C and angle CBE = 46 because they are congruent to angles D and DEB since ABED and FEBC are congruent.

    Instead of using the supplementary angles step, you could have computed angles A and ABE to be 134 since the four angles of a quadrilateral have to add up to 360, and these two angles are equal since they are part of an isosceles trapezoid. Then the four angles of ABED and FEBC are correspondingly congruent since the trapezoids are congruent.

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