NON ISOSCELES Trapzoid

Question

if JKLM is an isosceles trapezoid,find each missing angle M<J=

Answer 1

Question: In an isosceles trapezoid JKLM, find each missing angle M given

that angle J is greater than angle M.

Explanations:

In an isosceles trapezoid, the two non parallel sides (legs) are congruent, and the base angles are equal. Specifically, angles adjacent to each base are congruent.

Angle J and angle K are the base angles on one base.

Angle L and angle M are the base angles on the other base.

Since it's an isosceles trapezoid:

1. (< J = < K ) __________________________ Angle J = Angle K
2. symbol (<) stands for Angle
3. (<L = < M) ___________________________Angle L = Angle M

Step 1:

The sum of the interior angles in any quadrilateral is 360 degrees.

Therefore: <J + <K + <L + <M = 360 degrees

Substituting the equal angles: 2<J + 2<M = 360 degrees

Dividing both sides by 2:

<J + <M = 180 degrees

Step 2:

Solving for <M: <J + <M = 180 degrees

( Subtract <J from both Sides)

<M = 180 degrees - <J

Angle M = 180 degrees minus Angle J

Conclusion: Final Answer

Angle M = 180 degrees - Angle J

( <M = 180 degrees - < J )

Given that Angle J greater than Angle M, this equation ensures that Angle M is less than Angle J.

In an isosceles trapezoid, each pair of adjacent angles are supplementary. Therefore,

if one angle is known to be larger, the opposite angle can be found by subtracting the known

angle from 180 degrees.

I hope this information is useful. Please let me know if you require any more assistance. If anyone in my neighborhood is interested in setting up an in-person math tutoring session. I look forward to hearing from them. Have an amazing day. Doris H.