[tex]m\angle B= 41^{\circ},[/tex] [tex]m\angle F= 70^{\circ},[/tex] [tex]m\angle H = 61^{\circ},[/tex] [tex]m\angle K= 56^{\circ}.[/tex]
Step-by-step explanation:
Step 1:
The total of the angles in any triangle is 180°.
So to determine the third angle of the given triangles, we subtract the sum of the other two sides from, 180°.
The third angle = 180° - (the first angle + the second angle).
Step 2:
For triangle ABC,
[tex]m\angle B=180^{\circ}-(\angle A+\angle C)[/tex],
[tex]m\angle B=180^{\circ}-(83^{\circ} + 56^{\circ}) = 180^{\circ} - 139^{\circ} = 41^{\circ}.[/tex]
So [tex]m\angle B= 41^{\circ}.[/tex]
For triangle DEF,
[tex]m\angle F=180^{\circ}-(\angle D+\angle E)[/tex],
[tex]m\angle F=180^{\circ}-(61^{\circ} + 49^{\circ}) = 180^{\circ} - 110^{\circ} = 70^{\circ}.[/tex]
So [tex]m\angle F= 70^{\circ}.[/tex]
Step 3:
For triangle GHI,
[tex]m\angle H=180^{\circ}-(\angle G+\angle I)[/tex],
[tex]m\angle H=180^{\circ}-(49^{\circ} + 70^{\circ}) = 180^{\circ} - 119^{\circ} = 61^{\circ}.[/tex]
So [tex]m\angle H = 61^{\circ}.[/tex]
For triangle JKL,
[tex]m\angle K=180^{\circ}-(\angle J+\angle L)[/tex],
[tex]m\angle K=180^{\circ}-(83^{\circ} + 41^{\circ}) = 180^{\circ} - 124^{\circ} = 56^{\circ}.[/tex]
So [tex]m\angle K= 56^{\circ}.[/tex]
