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Trapezium ABCE is made from parallelogram ABCD
and isosceles triangle ADE.
A
B
106°
E
D
Work out the size of angle AED.

Trapezium ABCE Is Made From Parallelogram ABCD And Isosceles Triangle ADE A B 106 E D Work Out The Size Of Angle AED class=

Sagot :

thebecks

Answer:

Angle AED=32 degrees

Step-by-step explanation:

angle ADC=angle ABC because parallelogram

then angle ADC=106 degrees

angle EDA is supplementary to angle ADC (ADC+EDA=180 degrees)

then angle EDA=74 degrees

because triangle ADE is isosceles, angle EAD=angle EDA

since the total angles in a triangle =180 degrees,

Angle AED=180-2(74)=32 degrees

akposevictor

Applying the definition of isosceles triangle and parallelogram, the size of angle AED is: 32°.

Facts about Parallelogram and Isosceles Triangle

  • The opposite angles in a parallelogram have equal angle measures.
  • The two angles that are directly opposite the two equal sides in an isosceles triangle are congruent.

Thus:

m∠ABC = m∠ADC = 106° (opposite sides of parallelogram)

m∠ADC = 106°

m∠ADE = 180 - 106 = 74°

m∠AED = 180 - 2(74) (isosceles triangle)

m∠AED = 32°

Thus, applying the definition of isosceles triangle and parallelogram, the size of angle AED is: 32°.

Learn more about parallelogram on:

https://brainly.com/question/3050890

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