Answer: x = 9.611 ; or ; x = 9 11/18 .
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Explanation:
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All angles of any triangle must add up to 180 degrees.
So, (10x - 4) + (8x + 3) + 91 = 180 ; Solve for "x" ;
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10x - 4 + 8x + 3 + 81 = 180 ;
Combine the "like terms" on the left-hand side of the equation:
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+10x + 8x = 18x ;
- 4 + 3 + 8 = 7 ;
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18x + 7 = 180 ;
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Subtract "7" from each side of the equation:
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18x + 7 - 7 = 180 - 7 ;
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to get:
18x = 173 ;
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Divide EACH side of the equation by "18" ; to isolate "x" on one side of the equation; and to solve for "x" ;
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18x / 18 = 173 / 18 ;
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x = 9.6111111111111111....
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Write as: 9.611 ; or; 9 11/18.
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Your answer to this would be:
A) ∠3, ∠6, ∠7
∠3 is congruent to ∠2 because of the vertical angles theorem. This theorem states vertical angles (angles opposite each other) are congruent.
∠6 is congruent to ∠2 because of the corresponding angles theorem. This theorem states corresponding angles (angles that are in the same position as their correspondent) are congruent.
∠7 is congruent to ∠2 because of the alternate exterior angles theorem. This theorem states that alternate exterior angles (angles on opposite sides of the transversal and outside the two parallel lines) are congruent.
A) 36 inches and b) 78 inches squared
