Question

find angle CMN?
if AB = AC
BC= CM​

Answer 1

Step-by-step explanation:

Given:

angleCAX=139°

AB=AC

BC=CM

segCB||segNM

seg CM is angle bisector of angle ACB

To find:

angleCMN

Proof:

angle CAX+angle CAB= 180° .......

( angles in a linear pair)

139° + angle CAB= 180°

angle CAB= 180°-139

therefore,

angle CAB= 41° ...... (1)

In ∆ ABC,

angle ABC= angle ACB =x ° (2) ......

( Isosceles triangle theorem)

angle CAB+angle ABC + angle ACB=180°

....... ( sum of measure of all angles of a triangle is 180°)

41° +x°+x°= 180° .... [ from(1)&(2)]

x+x= 180-41

2x= 139

x= 139/2

x= 69°30'

therefore,

angle ABC= angle ACB= x°=69°30'

angle ACM = angle MCB = q° (3).......

( angle bisector theorem )

angle ACB= angle ACM + angle MCB

.....[from(3)] ( angle addition property)

therefore,

69°30'= q°+q°

69.30= 2q

q= 69.30/2

q= 34.65

therefore,

q°= 35°5'

therefore,

angle ACM= angle MCB= q°=35°5'

angle CMN= angle MCB .......

( Alternate angle theorem.

seg CB || segMN,

On transversal MC.)

therefore,

angle CMN= 35°5'