Find x ,,,, .....

Geometry Level 2

Solve for the value of x x in degrees.

9 ∘ 9^\circ 1 1 ∘ 11^\circ 1 0 ∘ 10^\circ 1 5 ∘ 15^\circ

Marvin Kalngan by Marvin Kalngan , 38, Philippines

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Maria Kozlowska
Oct 12, 2020

Reflect A and C on BD giving A' and C'. DA'=CA' and AA'=CA'. This makes AA'D equilateral. Angle DAA' = 6 x = 60. Therefore x=10.

1 Helpful 0 Interesting 1 Brilliant 0 Confused

OK, triangle BCD is isosceles (BC = DC) so reflecting around BD gives a rombus BCDC' so A' is on BC, DA = DA' and AC' = CA' but it's not so obvious for me why DA' = CA' or AA' = A'C.

Lu Ca - 7 months, 2 weeks ago

Using sine rule to the upper and lower triangles we get

2 sin ⁡ ( 3 x ) cos ⁡ ( 4 x ) − sin ⁡ ( 5 x ) = 0 2\sin (3x)\cos (4x)-\sin (5x)=0

Of the given options, only x = 10 ° x=\boxed {10\degree} satisfies this equation.

0 Helpful 0 Interesting 0 Brilliant 1 Confused

That doesn't rule out the possibility that there is another solution of x x .

Pi Han Goh - 8 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...