Question

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

Answer 1

Answer:

A. 44º

Step-by-step 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.