Triangle lmn is congruent to hij. Angle l measures 35 and angle m measures 65 and angle j measures 2x. Find the value of x
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To find the value of x, we need to use the fact that two triangles are congruent.
Since triangles LMN and HIJ are congruent, their corresponding angles are equal. Given that angle L measures 35 degrees and angle M measures 65 degrees, we can determine the measure of angle J in terms of x.
Since angle J in triangle HIJ corresponds to angle M in triangle LMN, we have:
angle J = angle M = 65 degrees
We also know that angle J in triangle HIJ measures 2x. So, we can set up the following equation:
2x = 65
To solve for x, we divide both sides of the equation by 2:
x = 65/2
Simplifying the right-hand side gives us:
x = 32.5
Therefore, the value of x is 32.5.
To find the value of x, we need to use the fact that corresponding angles of congruent triangles are equal.
Given that triangle LMN is congruent to triangle HIJ, we know that angle L is congruent to angle H, angle M is congruent to angle I, and angle N is congruent to angle J.
We are told that angle L measures 35 degrees, angle M measures 65 degrees, and angle J measures 2x.
Using this information, we can write the equation:
35 degrees = 2x
To solve for x, we need to isolate it on one side of the equation.
Divide both sides of the equation by 2:
35 degrees / 2 = 2x / 2
17.5 degrees = x
Therefore, the value of x is 17.5 degrees.
by similarity, N = J = 2x
since angles add up to 180, 35+65+N=180, so N=80
so, 2x=80, x=40