QuestionGiven is a line and . Find , , , and using given lengths and angles.
Studdy Solution
STEP 1
Assumptions1. is a straight line.
. .
3. The length of is3.
4. The measure of is35 degrees.
5. The measure of is120 degrees.
6. The length of is .
7. The length of is .
8. The lengths of and are unknown.
9. The measures of and are unknown.
STEP 2
Since , we know that their corresponding sides and angles are equal. Therefore, we have\angle BCA = \angleCD\angle BAC = \angleDC
STEP 3
Now, we can use the given values to find the measure of and \angleCD. We know that the sum of the angles in a triangle is180 degrees, so we have\angleCD =180^\circ - \angle DEC - \angleDC
STEP 4
Since and \angle BAC = \angleDC, we can substitute these values into the equations from3 to get\angleCD =180^\circ - \angle DEC - \angleDC =180^\circ -35^\circ - \angleDC
STEP 5
We know that \angle BCA = \angleCD, so we can set the two equations from4 equal to each other to get180^\circ -35^\circ - \angle BAC =180^\circ -35^\circ - \angleDC
STEP 6
olving the equation from5 gives us\angle BAC = \angleDC
STEP 7
We know that is a straight line, so \angle BAC + \angle CAD + \angleDC =180^\circ. Substituting and \angle BAC = \angleDC into this equation gives us
STEP 8
olving the equation from7 gives us\angle BAC = \angleDC =30^\circ
STEP 9
Now that we know , we can find .
STEP 10
Since , we know that and . Therefore, .
STEP 11
We also know that .
STEP 12
Since , we can set up the equation .
STEP 13
olving the equation from12 gives us .
STEP 14
Finally, we can find .
So, the unknowns are , , , and .
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