The value of x used in the expression for measurement of angle L is given by: Option C: 6.5
How are angles of isosceles triangles relate?
For any triangle, whether it be isosceles triangle or not, the sum of measurements of its angles is [tex]180^\circ[/tex]
The isosceles triangle consists two of its angle with same measurement. One of its angle which is not among those two equal measurement angles is called vertex angle.
Let we take [tex]\text{Measurement of vertex angle} = V^\circ[/tex]
Therefore, if we assume those two equal measurement angles being of [tex]D^\circ[/tex] measurement, then, we get:
[tex]D^\circ + D^\circ + V^\circ = 180^\circ\\\\2D + V = 180\\\\\\\text{Subtracting V from both the sides and then dividing by 2}\\\\D = \dfrac{180 - V}{2}[/tex]
For the given case, we've got:
- The triangle JKL being isosceles
- Angle J is vertex angle and [tex]m\angle J = 50^\circ[/tex]
(m before an angle shows that we're talking about its measurement).
Let other two angles L and K are therefore going to be of same measurement.
It is given that:
[tex]m\angle L = (8x + 13)^\circ[/tex]
Therefore, we get: [tex]m\angle K = (8x+13)^\circ[/tex]
Using the fact that all angles of a triangles add up to [tex]180^\circ[/tex]
Therefore,
[tex]8x + 13 + 8x + 13 + 50 = 180\\16x + 76 = 180\\16x = 180 - 76\\\\x = \dfrac{104}{16} = 6.5[/tex]
Thus, the value of x used in the expression for measurement of angle L is given by: Option C: 6.5
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