contestada

The sum of the measure of the angles of any triangle is 180 degrees. In triangle ABC, angles A and B have the same measure, while the measure of angle C is 48 degrees larger than each of A and B. What are the measures of the three angles?

Respuesta :

[tex] \bf \measuredangle B=\measuredangle A~\hspace{5em}\measuredangle C=\measuredangle A+48
\\\\[-0.35em]
~\dotfill\\\\
B+A+C=180\implies \stackrel{B}{A}+A+\stackrel{C}{A+48}=180\implies 3A+48=180
\\\\\\
3A=132\implies A=\cfrac{132}{3}\implies \boxed{A=44}
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
~\hspace{5em}A=44\qquad B=44\qquad C=44+48\implies C=92 [/tex]

altavistard

Take a clue from the info that Angles A and B have the same measure. Then the sum of Angles A and B is 2A (we have eliminated B). Now this 2A plus the measure of Angle C add up to 180 degrees: 2A + (A+48).

Then 2A + A + 48 = 180, or 3A = 228, or A = 76 degrees.

Thus, 180 - 2(76) = 28.

The three angles are as follows: A = B = 76 degrees, and C is 28 degrees.

Check: Do A, B and C sum up to 180 degrees, as they must?

Does 76 + 76 + 28 (degrees) add up to 180 (degrees)? Yes.

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