Final answer:
In the given triangle with congruent sides, if angle EAD is 18°, the value of x can be found to be 36°.
Step-by-step explanation:
In the triangle, AD is congruent to DE is congruent to EF is congruent to FG. If the measure of angle EAD is 18°, we can find the value of x.
Since AD is congruent to DE, we know that the angles EAD and ADE are equal. Therefore, angle ADE is also 18°.
Since EF is congruent to FG, we know that the angles EFG and FGE are equal. Therefore, angle FGE is also 18°.
Since the angles in a triangle add up to 180°, we can find angle EFG by subtracting the sum of angles EAD and ADE from 180°. Thus, angle EFG = 180° - 18° - 18° = 144°.
Similarly, we can find angle FGE by subtracting the sum of angles EFG and GEF from 180°. Thus, angle FGE = 180° - 144° - 18° = 18°.
Since angle FGE is congruent to angle DEF, we know that angle DEF is also 18°.
Finally, since angle DEF is congruent to angle DEG, we can find angle DEG by subtracting the sum of angles DEF and EFD from 180°. Thus, angle DEG = 180° - 18° - 18° = 144°.
Now, we can see that triangle DEG is an isosceles triangle with angles of 18°, 18°, and 144°. In an isosceles triangle, the base angles (the angles opposite the congruent sides) are equal. Therefore, angle EGD = angle EGD = 18°.
Since angle DEG is congruent to angle DFG, we know that angle DFG is also 144°.
Therefore, if all the angles in the triangle are known, we can calculate the value of x using the fact that the sum of the angles in a triangle is 180°.
x = 180° - 18° - 18° - 18° - 144° - 144° = 36°