Answer:
[tex] \displaystyle \angle4 = {108}^{ \circ} [/tex]
Step-by-step explanation:
we are given a triangle
and we want to figure out the missing exterior angle of the triangle
in order to so
remember
the straight line theorem
therefore we get:
[tex] \displaystyle {72}^{ \circ} + \angle4 = {180}^{ \circ} [/tex]
cancel 72° from both sides:
[tex] \displaystyle \angle4 = {108}^{ \circ} [/tex]
Alternate way:
recall that,
if a side of a triangle is extended then exterior angle so formed equal to the sum of the two opposite interior angles
so we acquire:
[tex] \displaystyle {51}^{ \circ} + {57}^{ \circ} = \angle4 [/tex]
simplify addition:
[tex] \displaystyle \angle4 = {108}^{ \circ} [/tex]
