HELP PLSSSSSSSSSSSSSSSSSSSSSQ

Question

asked Aug 8, 2021 71.0k views

1 Answer

Kulodo · Answer 1 · 2021-08-13T01:49:43+0000

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

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
$m\angle K= 56^(\circ).$