The measure of the exterior angle at vertex D is: D. 54°
<em><u>Recall:</u></em>
- The exterior angle theorem of a triangle states that the measure of an exterior angle equals the sum of the measures of two opposite interior angles of the triangle.
<em><u>Thus:</u></em>
In ΔDEF, (8x−2)º is an exterior angle at vertex D.
m∠E = (3x−8)° (interior angle)
m∠F = (4x+13)° (interior angle)
<em>Therefore:</em>
(8x−2)º = (3x−8)° + (4x+13)°
8x - 2 = 3x - 8 + 4x + 13
8x - 2 = 7x + 5
8x - 7x = 2 + 5
x = 7
Exterior angle at vertex D = (8x−2)º
= 8(7) - 2
= 54º (option D)
Learn more about exterior angle theorem on:
brainly.com/question/24756010
Assuming you want an expression for the possible total area of the patio: if "completed" would be a rectangle of dimensions n, m: each must be >=3 to allow for octagonal corners. But each of the 4 corners must be missing, that's diagonals comprising (1/2)a^2, (1/2)b^2, (1/2)c^2, and (1/2)d^2, where a,b,c, and d must be variously limited and co-limited so as to allow at least 1 linear side of the original rectangle to be exposed. So A = (n*m)-(1/2)a^2-(1/2)b^2-(1/2)c^2-(1/2)d^2 as an expression.
Now, imagine replicating your possible (potentially irregular) octagons onto a plane and juxtaposing them so as to create a paved network. What geometric properties might such a network have? You now have a miniscule idea what nature does with silicate networked minerals, except that takes place in 3-D, with tetrahedra of SiO4 .
Take Sin of 5 and subtract Cos 2
Sin 5 Cos -2
5-2=3
5x+3=3
√x=3
2x+5y+(1)z=3
