Mathematics: HELP PLSSSSSSSSSSSSSSSSSSSSSQ

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HELP PLSSSSSSSSSSSSSSSSSSSSSQ - id5527238, Mlmyers81

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21.01.2022

$m\angle B= 41^{\circ},$ $m\angle F= 70^{\circ},$ $m\angle H = 61^{\circ},$ $m\angle K= 56^{\circ}.$

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,

$m\angle B=180^{\circ}-(\angle A+\angle C)$ ,

$m\angle B=180^{\circ}-(83^{\circ} + 56^{\circ}) = 180^{\circ} - 139^{\circ} = 41^{\circ}.$

So $m\angle B= 41^{\circ}.$

For triangle DEF,

$m\angle F=180^{\circ}-(\angle D+\angle E)$ ,

$m\angle F=180^{\circ}-(61^{\circ} + 49^{\circ}) = 180^{\circ} - 110^{\circ} = 70^{\circ}.$

So $m\angle F= 70^{\circ}.$

Step 3:

For triangle GHI,

$m\angle H=180^{\circ}-(\angle G+\angle I)$ ,

$m\angle H=180^{\circ}-(49^{\circ} + 70^{\circ}) = 180^{\circ} - 119^{\circ} = 61^{\circ}.$

So $m\angle H = 61^{\circ}.$

For triangle JKL,

$m\angle K=180^{\circ}-(\angle J+\angle L)$ ,

$m\angle K=180^{\circ}-(83^{\circ} + 41^{\circ}) = 180^{\circ} - 124^{\circ} = 56^{\circ}.$

So $m\angle K= 56^{\circ}.$

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