Question

Please help with this problem!!!

Answer 1

Hi,

98°

Explanation:

In the triangle BCI:

`m\angle C=180^o-43^o-55^o=82^o\\m\angle C=m\angle FGI=82^o (corresponding\ angles)\\m\angleFGC=180^o-82^o=98^o\\`

Answer 2

`\sf m \angle FGC = 98 ^\circ`

Explanation:

Given:

`\sf m \angle I = 55^\circ`

`\sf m \angle FBC = 43^\circ`

To find:

`\sf m \angle FGC = ?`

Solution:

Since we can not find the angle
`\sf m \angle FGC` directly here, so,

Let's find the angle
`\sf m \angle IFG` first.

Since
`\sf m \angle IFG` and
`\sf m \angle FBC` are corresponding angle and corresponding angles are equal.

So,

`\sf m \angle IFG = m \angle FBC = 43^\circ`

We know that

Exterior angle of a triangle is equal to the sum of opposite two interior angle of a triangle.

So,

`\sf m \angle IFG + m \angle FIG = m\angle FGC`

Substitute the value:

`\sf 43^\circ + 55^\circ= m \angle FGC`

Simplify:

`\sf m \angle FGC = 98 ^\circ`

Therefore,

`\sf m \angle FGC = 98 ^\circ`