Answers:
- angle G = 25
- angle J = 107
- angle I = 48
- angle P = 25
- angle K = 107
- angle H = 48
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Explanation:
Triangle GJI and triangle PKH are similar triangles. The order of the letters is important because it tells us how the angles pair up.
The first letter of GJI is G, while the first letter of PKH is P. This means angles G and P pair up. They are congruent pair because similar triangles have congruent corresponding angles.
So,
G+P = 50
G+G = 50 .... plug in G = P
2G = 50
G = 50/2
G = 25
Both angle G and angle P are 25 degrees
Use angle I = 48 to help find angle J
G+J+I = 180
25+J+48 = 180
J+73 = 180
J = 180-73
J = 107
Angle J is 107 degrees
Since J and K are the second letters of GJI and PKH respectively, this means angle J = angle K = 107
Since I and H are the third letters of GJI and PKH respectively, we know that angle I = angle H = 48
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Summary:
- angle G = 25
- angle J = 107
- angle I = 48
- angle P = 25
- angle K = 107
- angle H = 48
