BD bisection angle ABC, be the angle ABC is divided into two parts of 2:5, angle DBE = 21 degrees, find the degree of angle ABC, do not unknown! urgent

BD bisection angle ABC, be the angle ABC is divided into two parts of 2:5, angle DBE = 21 degrees, find the degree of angle ABC, do not unknown! urgent

Angle abd equals half of angle ABC, and angle Abe equals two seventh of angle ABC, so angle DBE equals angle abd minus angle Abe equals fourteenth of triangle ABC
So the angle ABC is 21 / (3 / 14) = 98

It is known that ∠ ace = ∠ CDE = 90 °, point B is on CE, CA = CB = CD, through the circle intersection ab of a, C and D to f (as shown in the figure). It is proved that f is the heart of △ CDE

Proof: proof 1: as shown in the figure, if DF is connected, then FB = FD is obtained from the known, ∫ CDF = ∠ cab = 45 ° = 12 ∠ CDE, ∫ DF is the bisector of ∠ CDE, connecting BD and CF, and CD = CB, then ∫ FBD = ∠ cbd-45 ° = ∠ cdb-45 ° = ∠ FDB, that is, the distances from F to B, D and F are equal, and F is on the vertical bisector of BD, thus

In the triangle ABC, the angle ACB = 90 ° CD is perpendicular to AB and D, the point E is on AB, and AE = CE = 2, the angle ace = 30 ° to find the length of BD

In RT △ ABC, ∠ ACB = 90 °, CD ⊥ AB, intersection AB with D, point E on AB, AE = CE = 2, ∠ ace = 30 ° AE = CE = 2, ∠ CAE = ∠ ace = 30 ° = ∠ cab ⊥ ABC = 90 ° - ∠ CAE = 90 ° - 30 ° = 60 °, ∠ BCD = 30 ° through point E as eh ⊥ AC, intersection AC with H, ah = ch AC = 2CH = 2ce * cos ∠ ace = 2 * cos30 °

As shown in the figure, ∠ ABC = 30 ° in △ ABC, take BC and AC as sides, make equilateral △ BCD and equilateral △ ace, and connect be to verify: ab & # 178; + BC & # 178; = be & # 178;
Please use the method of connecting de (connecting ad. a little don't understand) fast, very urgent. Urgent!

Prove: connect ad, in △ BCE and △ DCA, BC = DC, CE = Ca, ∠ BCE = ∠ DCA, so △ BCE ≌ △ DCA, so ad = be, and because ∠ abd = ∠ ABC + ∠ CBD = 30 ° + 60 ° = 90 °, so AB & # 178; + BC & # 178; = AB & # 178; + BD & # 178; = ad & # 178; = be & # 178; don't forget to add points to me