Answer:
16. 80
17) 105 in^2
18) 90
Step-by-step explanation:
16. Angle bisector:
BC is an angle bisector. Angle bisector divides the angle into two equal angles.
∠ABC = ∠BCD
= 40°
∠ABD = ∠ABC + ∠BCD
= 40 + 40
= 80°
∠ABD = 80°
17.Area of the composite figure:
Area of rectangle ABCE = length * breadth
= 17 * 3
= 51 in²
ED = EC - DC
=17 - 8
= 9 in
FE = FA - EA
= 12 - 3
= 9 in
Area of square DEFG = side * side
= 9 * 9
= 36 in²
FG = 9 in
h = 4 in
[tex]\sf Area \ of \ triangle = \dfrac{1}{2}*base* height[/tex]
[tex]\sf = \dfrac{1}{2}* 9* 4 \\\\\\ = 9 * 2\\\\= 18 \ in^2[/tex]
Area of the figure = area of rectangle ABCE + area of square + area of triangle
= 51 + 36 + 18
= 105 in²
18: complementary angles:
Complementary angles add up to 90°.
∠ABD + ∠EBC = 90
50 + ∠EBC = 90
∠EBC = 90 - 50
∠EBC = 40°
∠DBE + ∠ABD + ∠EBC = 180 {Straight line angles}
∠DBE + 50 + 40 = 180
∠DBE + 90 = 180
∠DBE = 180 - 90
∠ DBE = 90°
