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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. 😊

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    $\begingroup$ We wish to see your picture, Thank you! $\endgroup$
    – Michael Rozenberg
    Aug 2, 2017 at 8:32
  • $\begingroup$ I couldn't figure out how to attach an image, only a link so I've added a description instead that describes where each angle is: "I am given one interior angle as 25 Another interior as x + 15 And the other is missing The final angle given is an exterior angle 3x - 10 that is opposite the two interior angles" $\endgroup$
    – Evangeline Elizabeth Rose Mitc
    Aug 5, 2017 at 3:10
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    $\begingroup$ Yes it's correct. $\endgroup$
    – Michael Rozenberg
    Aug 5, 2017 at 3:15
  • $\begingroup$ Thanks for your help, much appreciated! $\endgroup$
    – Evangeline Elizabeth Rose Mitc
    Aug 5, 2017 at 4:47
  • $\begingroup$ You are welcome! $\endgroup$
    – Michael Rozenberg
    Aug 5, 2017 at 4:56

1 Answer 1

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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 $115^{\circ}$.

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