Question

Solve for the unknown angle measure θ. A. θ=112.5 B. θ=120 C. θ=144 D. θ=150

Answer 1

Answer:

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 ,

$\bold{90 \degree + 90 \degree + \theta+ \theta+ \theta+ \theta+ \theta+ \theta = 1080 \degree }\\ \\ 180\degree + 6\theta = 1080\degree \\ \\ 6\theta = 1080\degree - 180\degree \\ \\ 6\theta = 900\degree \\ \\ \theta = \frac{900}{6} \\ \\ \underline\bold\pink{\: \theta = 150\degree}$

therefore ,

option ( D ) θ=150 is correct.

hope helpful :D

Answer 2

Solution:-

In the given polygon-

>>Two of the angles are of 90⁰

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

$\green{ \underline { \boxed{ \sf{(n-2)\times180}}}}$

Here number of sides,n = 8

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

$\sf \implies 6 \times 180$

$\sf \implies 1080 \degree$

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

$\implies \sf 1080- 2\times 90$

$\implies \sf 1080- 180$

$\implies \sf 900 \degree$

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

Also, 6$\theta$ = 900⁰

$\theta = \dfrac{900}{6}$

$\theta = 150 \degree$