Match the following items.

if ∠dbc = 40°, then

1. m∠ecb =
40
2. m =
80
3. m =
50
4. m∠dcf =
100

Step-by-step explanation:

Given:

°

From the triangle, using the theorem that center angle by an arc is twice the angle it subtend at the circumference.

Also, the diameter of the circle is BD. As per the theorem that says that angle subtended by the diameter at the circumference is always 90°,

From the Δ BCD, which is a right angled triangle,

Now, using the theorem that angle between the tangent and a chord is equal to the angle subtended by the same chord at the circumference.

Here, chords CD and BC subtend angles 40 and 50 at the circumference as shown in the diagram by angles and EF is a tangent to the circle at point C.

Therefore,

Again, using the same theorem as above,

Hence, all the angles are as follows:

1^3 + 2^3 + 3^3 +4^3 = (1+2+3+4)^2

step-by-step explanation:

i am only able to answer the first part. i am not sure about the second part. sorry