my son is in 6th grade and i am trying to help him solve this problem. but i want to understand so i can teach him.
Write and solve equations to determine the value of x and y .
triangle is given (PMN).
$M$ is $13x$, $N$ is 65 deg, $p$ is not given. length pm is 7/8in, MN not given, $PN$ is $Y+2/3$ in.
I watched some youtube videos but can't find one that is suitable for 6th grader. Please see attached.
One relation you can use is that the angles sum to $180^\circ$. $$ 180 = \alpha + 65 + (13 x) $$ I would split the angle $\alpha$, and the side $MN$, such that we get two rectangular triangles.
Interesting Deepaks remark about the dashes indicating a triangle with two equal sides seems to be true in the English speaking world, I see it used in the English language Wikipedia article (but not in the German one). The word isocles shows up in another problem on that image as well so it looks likely.
That simplifies the problem a lot. We have $$ 7/8 = y + 2/3 $$ and split $\alpha$ in the middle. So the relation for the other two angles gets very easy.
You know the triangle is isoceles (that's what those little dashes across the sides mean) with $PM = PN$.
Two properties of an isoceles triangle are important here.
1) two sides are equal in length - can you set up an equation involving $y$ that can be easily solved?
2) the two base angles are equal - can you set up an equation involving $x$ that can be easily solved?
