Answer:
52/3
Step-by-step explanation:
Use basic Thales therom,
Cross multiply,
3*(5x-8)=4*(3x+7)
3*5x - 3*8 = 4*3x + 4*7
15x - 24 = 12x +28
Add 24 to both sides
15x = 12x + 28 + 24
15x = 12x + 52
Subtract 12x from both sides
15x-12x =52
3x = 52
Divide both sides by 3
x = 52/3
The value of x is 120°
Explanation:
It is given that ABC is a straight line.
Also, ∠CBE = 20° and ∠CAF = 40°
We need to determine the value of ∠DBE
Let ∠DBE = x
Since, ∠CAF and ∠ABD are alternate interior angles.
By the alternate interior angles theorem, "if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are equal".
Thus, ∠CAF and ∠ABD are equal.
Hence, ∠CAF = ∠ABD = 40°
Since, we know that, the angles in a straight line add up to 180°, we have,
∠ABD + ∠DBE + ∠CBE = 180°
Substituting the values, we get,
40° + x + 20° = 180°
Adding, we have,
60° + x = 180°
Subtracting both sides by 60, we have,
x = 120°
Thus, the value of x is 120°
