I think I have solved this question but want to check if I am correct with my formula
I used the theorem (rule) : the measure of the exterior angle of a triangle is equal to the sum of the remote (opposite) interior angles.
My workings as follows:
I am given one interior angle as $25^{\circ}$.
Another interior as $x + 15^{\circ}$ and the other is missing.
The final angle given is an exterior angle $3x – 10^{\circ}$ that is opposite the two interior angles.
$x+ 15^{\circ} + 25^{\circ}$ (opposite interior angles) $= 3x – 10^{\circ}$ (exterior angle).
\begin{align*}
x + 15^{\circ} + 25^{\circ} & = 3x – 10^{\circ}\\
x – x + 15^{\circ} + 25^{\circ} + 10^{\circ} & = 3x – 10^{\circ} + 10^{\circ} – x\\
50^{\circ} & = 2x\\
\frac{50^{\circ}}{2} & = \frac{2x}{2}\\
25^{\circ} & = x\\
x & = 25^{\circ}
\end{align*}
So one of the interior angles is a
Ready given in this question which is: $25$ degrees
And the other given is: $x + 15^{\circ}$.
So if $x=25^{\circ}$ then this angle $= 40$ degrees.
And the exterior angle is
$3 \times 25 – 10 = 65$ degrees.
Am I correct in this working?
Thanks in advance. 😊
Best Answer
Yes, it's correct. $$x+15^{\circ}+25^{\circ}=3x-10^{\circ}$$ or $$x=25^{\circ},$$ which gives measured angles of the triangle: $25^{\circ}$, $40^{\circ}$ and $115^{\circ}$.