Abc is a triangle in which angle b = 2 angle c. d is a point on side bc such that ad bisects angle bac and ab = cd. prove that angle bac equal to 72 degrees

Step-by-step explanation:

In ΔABC, we have,

∠B=2∠C or ∠B=2y where ∠C=y

AD is the bisector of ∠BAC. So, Let ∠BAD=∠CAD=x

Let BP be the bisector of ∠ABC.

In ΔBPC, we have

∠CBP = ∠BCP = y ⇒ BP = PC ... (1)

Now, in ΔABP and ΔDCP, we have

∠ABP = ∠DCP = y

AB = DC [Given]

and, BP = PC [Using (1)]

So, by SAS congruence criterion, we have

Δ ABP ≅ Δ DCP

Therefore

∠BAP = ∠ CDP = 2x and AP = DP ,

So in Δ APD, AP=DP

=> ∠ADP = ∠DAP = x

In ΔABD, we have

∠ADC = ∠ABD + BAD ⇒ 3x= 2y + x

⇒ x = y

In ΔABC, we have

∠A + ∠B + ∠C = 180°

⇒ 2x + 2y + y = 180°

⇒ 5x = 180°

⇒ x = 36°

Hence, ∠BAC = 2x = 72°

step-by-step explanation:

the red lines denote the population of the bacteria after 35 hours. that would be 2,409.24. the y-intercept is the blue line which is 800 because that is the starting point. the equation used to make the graph is 800(1.032)^h, where h is the number of hours.

step-by-step explanation: