Discussion
M is a point on side AB of a triangle ABC such that AM = BM = CM. If angles A and B are respectively x and 70°, then the value of \((3x + 25^{\circ})\) is equal to :
Answer: B
The value of \(3x + 25^{\circ}\) is 85°.
Since AM = CM, ∠ACM = ∠A = x, and since BM = CM, ∠BCM = ∠B = 70°. So ∠C = x + 70°. Using the angle sum of triangle ABC:
\[ \begin{aligned} x + 70 + (x + 70) &= 180 \\ 2x &= 40 \Rightarrow x = 20 \\ 3x + 25 &= 60 + 25 = 85 \end{aligned} \]
The shortcut: M is equidistant from A, B and C, so it is the midpoint of the hypotenuse and ∠C = 90°, giving x = 20 directly.
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