Question

Solve for 44.
4 4 = [?]
510
51
44/42

Answer 1

`\displaystyle \angle4 = {108}^( \circ)`

Explanation:

the sum of the interior angles of a triangle is 180°

thus our equation is

`\displaystyle {51}^( \circ) + {51}^( \circ) + \angle2 = {180}^( \circ)`

simplify addition:

`\displaystyle {102}^( \circ) + \angle2 = {180}^( \circ)`

cancel 102° from both sides:

`\displaystyle \angle2 = {72}^( \circ) \cdots \text{I}`

By straight line theorem we acquire:

`\displaystyle \angle4 + \angle2 = {180}^( \circ)`

substitute:

`\displaystyle \angle4 + {72}^( \circ) = {180}^( \circ)`

cancel 72° from both sides:

`\displaystyle \angle4 = {108}^( \circ)`

hence, the measure of
`\angle 4` is 108°

Answer 2

Angle 4 is an exterior angle which is equal to the sum of the two opposite inside angles.

The two opposite inside angles are given as 51 and 51

Angle 3 = 51 + 51 = 102 degrees.