Question

Solve for the unknown angle measure θ.

A. θ=112.5
B. θ=120
C. θ=144
D. θ=150

Answer 1

Solution:-

In the given polygon-

>>Two of the angles are of 90⁰

The sum of all angle in n-sided polygon is given by -

`\green{ \underline { \boxed{ \sf{(n-2)*180}}}}`

Here number of sides,n = 8

So ,the sum of all angle =
`\sf (8-2)* 180`

`\sf \implies 6 * 180`

`\sf \implies 1080 \degree`

>>Since two of the angles are of 90⁰ ,let's subtract them from total angle sum to get angles in term of
`\theta` only.

`\implies \sf 1080- 2* 90`

`\implies \sf 1080- 180`

`\implies \sf 900 \degree`

Now, Sum of remaining 6 angles = 6
`\theta`

Also, 6
`\theta` = 900⁰

`\theta = (900)/(6)`

`\theta = 150 \degree`

Answer 2

heya ^^

let's first see what the question says -

so , we're given an octagon and the figure states that two of the angles of the octagon are of measure 90°.

while , rest of the angles have been named
`\bold{\theta }` and this thing clears that all the other angles are of equal measure.

now , angle sum property of octagon states that the sum of all the angles of an octagon equals 1080.

therefore ,

`\bold{90 \degree + 90 \degree + \theta+ \theta+ \theta+ \theta+ \theta+ \theta = 1080 \degree }\\ \\ 180\degree + 6\theta = 1080\degree \\ \\ 6\theta = 1080\degree - 180\degree \\ \\ 6\theta = 900\degree \\ \\ \theta = (900)/(6) \\ \\ \underline\bold\pink{\: \theta = 150\degree}`

therefore ,

option ( D ) θ=150 is correct.

hope helpful :D