Question

Find the measure of F. A. 44 B. 88 C. 90 D. 46

Answer 1

A. 44º

Explanation:

The sum of internal angles in a triangle is equal to 180 degrees, whereas the sum for a square is equal to 360 degrees. Given that three triangles depicted on figure constructs a square, it is to conclude that each is an isosceles triangle. The following relations are presented:

1)
`e + 92^(\circ) = 180^(\circ)` Given

2)
`a = b`,
`c = d` Given

3)
`a + b + 92^(\circ) = 180^(\circ)` Given.

4)
`c + d + e = 180^(\circ)` Given.

5)
`b + c = 90^(\circ)` Given.

6)
`2\cdot a + 92^(\circ) = 180^(\circ)` 2) in 3)

7)
`a = 44^(\circ)` Algebra

8)
`b = 44^(\circ)` By 2)

9)
`b= f` Alternate internior angles.

10)
`f = 44^(\circ)` By 8). Result

Hence, the answer is A.