Answer:
177°
Explanation:
A sector is the area between two radi.
We are given the perimeter of the sector as 21.4cm and the radius 4.2cm. Subtracting two radi from the perimeter will give us the arc of the sector as 13.
As we know, the formula for the length of an arc is: length of arc = ∅/360 × πd. Diameter is double the radius so in this case it's 8.4; so filling in the blanks our new formula is: 13 = ∅/360 × 8.4π.
We are trying to find ∅ which is the degree of the sector. So from this formula we can rearrange it by dividing 8.4π on both sides of the equation giving ¹³/8.4π = ∅/360; from here we multiply 360 on both sides and therefore getting ∅ on its own therefore allowing us to equate it.
Plug that all into a calculator and you get 177.3440794 so you can round it down to 177°
I saw this question a few minutes ago but spent a bit of time calculating it...sorry :)