Question

Micahdisu please help

Answer 1

Answer:

1) A - 42°

2) 74°

3) B - 45°

4) B - 66°

Step-by-step explanation:

1) E = D+H

87 = 45 + H

H = 42°

2) 180 - 50 - D

D = 180 - 44 - 62 = 74°

3) F = 105

H = 180-105 = 75

I + H = C + E

I + 75 = 83 + 37

I = 45°

4) D = 180 - (E + F)

D = 180 - (30 + 57) = 93°

93 = A + 27

A = 66°

Answer 2

Answer: In figure 1, angle H = 42°. In figure 2, angle F = 56°. In figure 3, angle I = 45° and in figure 4, angle A = 66°

Step-by-step explanation: Please refer to the attached diagram for details.

From figure 1, if angle E measures 87, then angle F would be calculated as

Angle F = 180 - 87 {Sum of angles on a straight line equals 180}

Angle F = 93

Then looking at triangle FHD, we have angles D and F as 45 and 93. Angle H = 180 - (45 + 93) {Sum of angles in a triangle equals 180}

Angle H = 180 - 138

Angle H = 42

From figure 2, if triangle ACB has two angles given as 44 and 62, then the third angle C, would be calculated as

Angle C = 180 - (44 + 62) {Sum of angles in a triangle equals 180}

Angle C = 180 - 106

Angle C = 74

Note that angle D equals angle C {Opposite angles are equal}. So if angle D measures 74, then looking at triangle FED, we have two angles already, E and D which are 50 and 74. To calculate angle F, the equation would be

f = 180 - 50 - 74

f = 56

That is, angle F = 56.

From figure 3, we have angles C and E given as 83 and 37. To calculate angle G

Angle G = 180 - (83 + 37) {Sum of angles on a straight line equals 180}

Angle G = 180 - 120

Angle G = 60

Also, to calculate angle H,

Angle H = 180 - 105 {Sum of angles on a straight line equals 180}

Angle H = 75

Looking at triangle GHI, we have identified two angles which are 60 and 75. To calculate the third angle which is angle I,

Angle I = 180 - (60 + 75) {Sum of angles in a triangle equals 180}

Angle I = 180 - 135

Angle I = 45

From figure 4, if angles B and E measure 27 and 30 respectively then the whole of that angle measures 27 + 30 which equals 57.

So looking at the biggest of all three triangles, two angles have been identified which are angles F and {B + E}

To calculate angle A

Angle A = 180 - (57 + 57) {Sum of angles in a triangle equals 180}

Angle A = 180 - 114

Angle A = 66.