Answer:
The range of values for x is; 5 < x < 29
Step-by-step explanation:
The given parameters are;
[tex]\overline {AB}[/tex] = 15
[tex]\overline {AD}[/tex] = 18
[tex]\overline {BC}[/tex] = [tex]\overline {CD}[/tex] Given
[tex]\overline {AC}[/tex] = [tex]\overline {AC}[/tex] by reflexive property
∠BCA = 2·x - 10
∠DCA = 48°
Since 15 < 18, given the common sides of the tringle ΔABC and triangle ΔADC, angle ∡(2·x - 10)° < 48°
Therefore;
2x - 10 < 48
2·x < 48 + 10
∴ x < 29
Also, given that 2·x - 10 is real, 0 < 2·x - 10
10 < 2·x
10/2 < x
5 < x
Therefore, an acceptable range is 5 < x < 29
