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QuestionFind the missing angle in triangles ABE and DEC where ∠ABE=25∘\angle ABE=25^{\circ} and ∠EDC=100∘\angle EDC=100^{\circ}.

Studdy Solution

STEP 1

Assumptions1. AC is a straight line with as the midpoint. . Two triangles, ABE and DEC, are formed above the line AC.
3. Point B is located on the left side of point A and point D is located on the left side of point.
4. ∠AB=25∘\angle A B=25^{\circ} and ∠DC=100∘\angle D C=100^{\circ}.
5. We are looking for the value of the missing angle.

STEP 2

First, we need to understand that the sum of the angles on a straight line is 180∘180^{\circ}. This is a fundamental property of Euclidean geometry.

STEP 3

We can use this property to find the value of ∠BC\angle B C. Since is the midpoint and ∠AB=25∘\angle A B=25^{\circ}, then ∠BC=180∘−25∘\angle B C =180^{\circ} -25^{\circ}.

STEP 4

Calculate the value of ∠BC\angle B C.
∠BC=180∘−25∘=155∘\angle B C =180^{\circ} -25^{\circ} =155^{\circ}

STEP 5

Now, we can use the same property to find the value of the missing angle. Since ∠DC=100∘\angle D C=100^{\circ}, then the missing angle = 180∘−100∘180^{\circ} -100^{\circ}.

STEP 6

Calculate the value of the missing angle.
Missing angle=180∘−100∘=80∘Missing\, angle =180^{\circ} -100^{\circ} =80^{\circ}However, this is not the final answer. We need to subtract ∠BC\angle B C from the missing angle to get the final answer.

STEP 7

Calculate the final value of the missing angle.
Final missing angle=Missing angle−∠BCFinal\, missing\, angle = Missing\, angle - \angle B C

STEP 8

Plug in the values for the missing angle and ∠BC\angle B C to calculate the final missing angle.
Final missing angle=80∘−155∘Final\, missing\, angle =80^{\circ} -155^{\circ}

STEP 9

Calculate the final missing angle.
Final missing angle=80∘−155∘=−75∘Final\, missing\, angle =80^{\circ} -155^{\circ} = -75^{\circ}This result is not possible in this context as angles cannot be negative. There seems to be a mistake in the calculation. Let's go back to5.

STEP 10

The correct calculation should be the missing angle = ∠BC−∠DC\angle B C - \angle D C.

STEP 11

Calculate the value of the missing angle.
Missing angle=∠BC−∠DCMissing\, angle = \angle B C - \angle D C

STEP 12

Plug in the values for ∠BC\angle B C and ∠DC\angle D C to calculate the missing angle.
Missing angle=155∘−100∘Missing\, angle =155^{\circ} -100^{\circ}

STEP 13

Calculate the missing angle.
Missing angle=155∘−100∘=55∘Missing\, angle =155^{\circ} -100^{\circ} =55^{\circ}The value of the missing angle is 55∘55^{\circ}, which is not among the options given. Therefore, the answer is. none of these.

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