Question

Tom erases the angle measures and lengths and tries again. Now he wants to label the triangleso that m

Answer 1

The triangle is real and it is an isosceles triangle.

The angles are: m

Step-by-step explanation

Step 1: Given:

`\begin{gathered} m\angle A\text{ = }(1)/(2)m\angle B \\ m\angle A\text{ = }(1)/(2)m\angle C \end{gathered}`

Step 2: Determine m

For m

`\begin{gathered} m\angle A\text{ = }(1)/(2)m\angle B \\ m\angle B\text{ = 2}* m\angle A \end{gathered}`

For m

`\begin{gathered} m\angle A\text{ = }(1)/(2)m\angle C \\ m\angle C\text{ = 2}* m\angle A \end{gathered}`

Step 3: Determine the measure of m

Recall: Sum of interior angles of a triangle is 180 degrees

`\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{ = }(180)/(5) \\ m\angle A=36^0 \end{gathered}`

For m

`\begin{gathered} m\angle B\text{ = 2}* m\angle A \\ m\angle B\text{ = 2}*36 \\ m\angle B\text{ = }72^0 \end{gathered}`

For m

`\begin{gathered} m\angle C\text{ = 2}* m\angle A \\ m\angle C\text{ = 2}*36 \\ m\angle C\text{ = }72^0 \end{gathered}`

Hence, the triangle is real and it is an isosceles triangle; the angles are: m