1) The best way to tackle questions like these is to sketch out:
2) We were told that this is an isosceles triangle therefore at least 2 of their angles are congruent to themselves. Therefore we can write down the following equation also considering the Triangle Sum Theorem:
[tex]\begin{gathered} 5x+24+5x+24+2x+72=180 \\ 12x+48+72=180 \\ 12x+120=180 \\ 12x+120-120=180-120 \\ 12x=60 \\ \frac{12x}{12}=\frac{60}{12} \\ x=5 \end{gathered}[/tex]Note that now, we can find the measure of each angle by plugging x=5:
[tex]\begin{gathered} m\angle A=m\angle B=5x+24=5(5)+24=49^{\circ} \\ m\angle A=m\angle B=49^{\circ} \\ m\angle C=2(5)+72 \\ m\angle C=82^{\circ} \end{gathered}[/tex]3) Thus the answer is:
[tex]m\angle A=49^{\circ},m\angle B=49^{\circ},m\angle C=82^{\circ}[/tex]
