Answer: x = -4 ; Angle = 60°
Concept:
The given figure is a triangle with 3 arc signs on each angle. This arc sign stands for the corresponding angles are congruent, which in this question, it shows that all three angles are congruent. Sometimes, if the figure has multiple angles and there are different groupings of congruent angles, then we use different numbers of arcs or symbols.
Solve:
Given information
An angle = 3x + 72
Total measure of angles = 180 (triangle angle sum theorem)
Total number of congruent angles = 3
Given expression
Total measure = Total number of congruent angles × An angle measure
Substitute values into the expression
180 = 3 (3x + 72)
Divide 3 on both sides
180 / 3 = 3 (3x + 72) / 3
60 = 3x + 72
Subtract 72 on both sides
60 - 72 = 3x + 72 - 72
-12 = 3x
Divide 3 on both sides
-12 / 3 = 3x / 3
[tex]\boxed{x=-4}[/tex]
Find the angle measure
3x + 72 = 3 (-4) + 72 = [tex]\boxed{60}[/tex]
Hope this helps!! :)
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