Asked by Shinobi
In the diagram below of triangle A, B, CABC, DD is the midpoint of start overline, A, C, end overline
AC
and EE is the midpoint of start overline, B, C, end overline
BC
. If mangle, C, B, A, equals, 5, x, plus, 48∠CBA=5x+48, and mangle, C, E, D, equals, 87, minus, 8, x∠CED=87−8x, what is the measure of angle, C, B, A∠CBA?
AC
and EE is the midpoint of start overline, B, C, end overline
BC
. If mangle, C, B, A, equals, 5, x, plus, 48∠CBA=5x+48, and mangle, C, E, D, equals, 87, minus, 8, x∠CED=87−8x, what is the measure of angle, C, B, A∠CBA?
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Answered by
GPT 3.5
Since D is the midpoint of AC, we can use the midpoint theorem to determine that angle DCE is equal to angle ECB. Therefore, angle ECD is equal to angle ECB + angle DCE = 2 * angle ECB.
Since E is the midpoint of BC, angle ECD is equal to angle CBA. Therefore, 2 * angle ECB = angle CBA.
Given that angle CBA = 5x + 48 and angle CED = 87 - 8x, we can set up the following equation:
5x + 48 = 2 * (87 - 8x)
5x + 48 = 174 - 16x
21x = 126
x = 6
Therefore, angle CBA = 5(6) + 48 = 30 + 48 = 78 degrees.
The measure of angle CBA is 78 degrees.
Since E is the midpoint of BC, angle ECD is equal to angle CBA. Therefore, 2 * angle ECB = angle CBA.
Given that angle CBA = 5x + 48 and angle CED = 87 - 8x, we can set up the following equation:
5x + 48 = 2 * (87 - 8x)
5x + 48 = 174 - 16x
21x = 126
x = 6
Therefore, angle CBA = 5(6) + 48 = 30 + 48 = 78 degrees.
The measure of angle CBA is 78 degrees.
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