m<wyz =(2x-5)° and m<XYW = (3x + 10)° .
Find the value x.
To find the value of x, we need to set up an equation based on the given information.
From the problem statement, we know that m<wyz is equal to (2x - 5) degrees and m<XYW is equal to (3x + 10) degrees.
Since we're dealing with angles, we can use the fact that the sum of the interior angles of a triangle is always 180 degrees.
In triangle XYZ, the sum of the angles m<wyz, m<XYW, and m<ZXY must equal 180 degrees.
Therefore, we can set up the equation:
(2x - 5) + (3x + 10) + m<ZXY = 180
Simplifying the equation:
5x + 5 + m<ZXY = 180
Next, we need to determine the measure of m<ZXY. If XYZ is a triangle, then the sum of its angles is also equal to 180 degrees.
So, we have:
(2x - 5) + (3x + 10) + m<YXZ = 180
5x + 5 + m<YXZ = 180
Now, we can set these two equations equal to each other:
5x + 5 + m<ZXY = 5x + 5 + m<YXZ
Since both 5x + 5 terms are the same, we can cancel them out:
m<ZXY = m<YXZ
Since the two angles are equal, we can represent them with the same variable:
m<ZXY = m<YXZ = y
Now, let's substitute the value of y into our previous equation:
5x + 5 + y = 5x + 5 + y
The equation is an identity, meaning that it holds true for all values of x and y. This implies that the value of x can be any real number.
Therefore, there is no unique value of x that satisfies the given conditions. The solution is x belongs to the set of real numbers.