An angle measures 62.8° less than the measure of its supplementary angle. What is the measure of each angle?
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well if 18 out of 25 like it, then the remaining 7 doesn't like it, namely 7 out of 25.
if we take 25 to be the 100%, what is 7 off of if in percentage?
Answer: x = 2
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Explanation:
Refer to the diagram below.
I've added points D,E,F,G. This helps with labeling the segments and angles, and identifying the proper triangles (to see which are congruent pairs).
Triangle GEA is congruent to triangle GFA. We can prove this using the AAS congruence theorem. We have AG = AG as the pair of congruent sides, and the congruent pairs of angles are marked in the diagram (specifically the blue pairs of angles and the gray right angle markers)
Since triangle GEA is congruent to triangle GFA, this means the corresponding pieces segment GF and GE are the same length.
The diagram shows GF = 3x-4, so this means GE = 3x-4 as well.
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Through similar steps, we can show that triangle GEC is congruent to triangle GDC. We also use AAS here as well.
The congruent triangles lead to GD = GE. So GD = 3x-4. The diagram shows that GD = 6x-10
Since GD is equal to both 3x-4 and 6x-10, this must mean the two expressions are equal.
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Now let's solve for x
6x-10 = 3x-4
6x-3x = -4+10
3x = 6
x = 6/3
x = 2
