In triangle ABC, points N and M lie on sides AB and AC, respectively. Given AM = AN = BM = NC = BC, find m∠BAC.

  36°

Step-by-step explanation:

Please refer to the attached figure.

Triangles ANC, AMB, BCN, CBM are all isosceles by virtue of the given congruences. By symmetry, we also claim that ΔABC is isosceles (AB≅AC).

We aren't sure how their internal angles relate, but we can write a couple of equations.

Let x = m∠BAC, y = m∠BCN.

∠NCA = ∠NAC  = ∠MBA = ∠MAB = x

∠BCM = ∠BMC = x +y

∠BMC = ∠MBA +∠MAB = 2x

So, we have ...

  ∠BMC = x +y = 2x   ⇒    y = x

And the sum of angles around ΔABC is ...

  x +(2x) +(2x) = 180°

  x = 180°/5 = 36°

The measure of angle BAC is 36°.

the first one

step-by-step explanation:

just id the test.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).