In a triangle ABC, the interior cevian CM is drawn, so that C M = A B ; Knowing th

Davian Lawson

Davian Lawson

Answered question

2022-05-02

In a triangle ABC, the interior cevian CM is drawn, so that C M = A B ; Knowing that the measure of A = 30 ° and B = 100 ° . Calculate the measure of M C B .

Answer & Explanation

Salvador Ayala

Salvador Ayala

Beginner2022-05-03Added 10 answers

Step 1
Draw AD parallel and equal to MC. Draw the line CE through D parallel and equal to AB. Complete the parallelogram ABCE. Drop perpendiculars from E and B onto CM and AD respectively. Mark the foot of first one G and second one H. The line AH crosses CM at J, and EG crosses AD at K. Quadrilateral GKHJ is a rectangle. This indicates that BH and EG are bisectors of angles M B C and A E C . Also, BG bisects M B C and is perpendicular to CM, which means that triangle BCM is isosceles. Therefore
θ = B M C = B C M = 180 100 2 = 40 . .
Update: the figure is correct. Consider this fact:
The bisectors of the angles in a parallelogram construct a rectangle.

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