Answer:
[tex]25.7^\circ [/tex] , [tex] 51.4^\circ[/tex] and [tex]102.9^\circ[/tex]
Step-by-step explanation:
Let the measures of the angles of the triangle be x, 2x, and 4x, where x is a positive constant.
According to the properties of triangles, the sum of the angles in any triangle is always 180 degrees.
So, we can write the equation:
[tex]x + 2x + 4x = 180^\circ[/tex]
Solving for x:
[tex]7x = 180^\circ[/tex]
[tex]x = \dfrac{180^\circ}{7} [/tex]
[tex] x =25.71428571 ^\circ[/tex]
[tex] x = 25.7^\circ [/tex]
Now, we can find the measures of each angle:
[tex]2x = 2 \times 25.71428571 ^\circ = 51.42857143 = 51.4 ^\circ[/tex]
[tex]4x = 4 \times 25.71428571 ^\circ =102.8571429 = 102.9 ^\circ[/tex]
Therefore, the angles of the triangle are [tex]25.7^\circ [/tex] , [tex] 51.4^\circ[/tex] and [tex]102.9^\circ[/tex]
