Question

please answer my maths questions
1. In square ABCD, point E is chosen in the interior of DABCD so that AEBC is equilateral. Let BD intersect EC in P. Find mZEPD. 2. In AABC, mZBAC = 80. The bisectors of ZABC and ZACB intersect each other at point I, then find mZBIC. 3. In AABC, BE and CF are altitudes and intersect at H. If mZBAC = 70 then find mZBHC. 4. AB is a diameter of a circle with center M. C is a point on the circle. If mZACM = 20, then find m2ABC. 5. AB is a diameter of a circle with center M. C is a point on the circle. If mZCMB = 48, then find mZACM. 6. In AABC, the bisector of ZBAC cuts BC at D, if ZABC = x and ZACB = y, find mZADC in terms of x,y. 7. Each angle of a polygon is 140; how many sides does it have ? 8. The sum of the interior angles of an n-sided convex polygon is double the sum of the exterior angles. Find n.​

Answer 1

Answer

REF.Image

△BEC is an equilateral △le

⇒BE=EC=BC

But BC=CD(ABCD is a square)

⇒EC=CD⇒∠CED=∠CDE

In △ECD,∠CED+∠CDE+90+60=180

⇒2∠CED=30⇒∠CED=15

∘

∠BEC=60

∘

⇒x=60−15=45

solution