Respuesta :
ANSWER
The triangle is real and it is an isosceles triangle.
The angles are: m
EXPLANATION
Step 1: Given:
[tex]\begin{gathered} m\angle A\text{ = }\frac{1}{2}m\angle B \\ m\angle A\text{ = }\frac{1}{2}m\angle C \end{gathered}[/tex]Step 2: Determine m
For m
[tex]\begin{gathered} m\angle A\text{ = }\frac{1}{2}m\angle B \\ m\angle B\text{ = 2}\times m\angle A \end{gathered}[/tex]For m
[tex]\begin{gathered} m\angle A\text{ = }\frac{1}{2}m\angle C \\ m\angle C\text{ = 2}\times m\angle A \end{gathered}[/tex]Step 3: Determine the measure of m
Recall: Sum of interior angles of a triangle is 180 degrees
[tex]\begin{gathered} m\angle A\text{ + m}\angle B\text{ + m}\angle C=180^0 \\ m\angle A\text{ + 2m}\angle A\text{ + 2m}\angle A=180^0 \\ 5m\angle A=180^0 \\ m\angle A\text{ = }\frac{180}{5} \\ m\angle A=36^0 \end{gathered}[/tex]For m
[tex]\begin{gathered} m\angle B\text{ = 2}\times m\angle A \\ m\angle B\text{ = 2}\times36 \\ m\angle B\text{ = }72^0 \end{gathered}[/tex]For m
[tex]\begin{gathered} m\angle C\text{ = 2}\times m\angle A \\ m\angle C\text{ = 2}\times36 \\ m\angle C\text{ = }72^0 \end{gathered}[/tex]Hence, the triangle is real and it is an isosceles triangle; the angles are: m
