Suppose CED = DBC. If m<EDC=63 degrees and m<DBC=82 degrees, what is m<DCE? Possible answers are 63, 82,145 or 35 degrees.
GHF = LJK by HL? if so state all of the congruent parts that allow the use of HL.
Possible answers Yes, <G= <L, GH=LJ,HF=Jk
Yes, <g=<L, GH=LJ.
Yes, <F=<K, GH=LJ.
Yes,<F=<K, GH=LJ,HF=LK.
35
To find the measure of <DCE, we can use the fact that the angles of a triangle add up to 180 degrees.
Given that CED = DBC, it implies that the triangle CED is congruent to the triangle DBC by the angle-angle criterion. Therefore, the corresponding angles are congruent.
We know that m<EDC = 63 degrees and m<DBC = 82 degrees. Since CED = DBC, it follows that m<CED = m<DBC = 82 degrees.
To find m<DCE, we can subtract the measures of the known angles from 180 degrees since the angles of a triangle add up to 180 degrees.
m<DCE = 180 - (m<EDC + m<CED)
m<DCE = 180 - (63 + 82)
m<DCE = 180 - 145
m<DCE = 35 degrees
Therefore, the measure of <DCE is 35 degrees.
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For the second question, to determine if GHF is congruent to LJK by HL (Hypotenuse-Leg), we need to establish if the two triangles have congruent hypotenuses and congruent legs.
The HL congruence criterion states that if the hypotenuse and one leg of one right triangle are respectively congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.
To apply HL congruence, we need to show that GH = LJ (congruent hypotenuses) and HF = JK (congruent legs).
From the given options, the only choice that satisfies this is: Yes, <G= <L, GH=LJ, and HF=JK.
Therefore, to use HL congruence, the congruent parts required are that <G = <L, GH = LJ, and HF = JK.