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.
