The angles in a triangle add up to 180º.
This is no different when the angles are algebraic expressions.
Form an equation from the angles shown in this triangle and solve it to find the value of a.
The sum of the angles = 180
a + 10 + a - 37 + a = 180
We simplify and solve this equation as follows:
3a - 27 = 180
3a = 207
a = 207 ÷ 3 = 69
a = 69º
From this we can then work out what each angle is:
The top angle is 69º
The angle below that is a + 10 = 69 + 10 = 79º
The final angle is a - 37 = 69 - 37 = 32º
Finally, add them altogether just to check that they do add up to 180:
69 + 79 + 32 = 180º
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