Question

HELP PLSSSSSSSSSSSSSSSSSSSSSQ

Answer 1

`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).`