Question

Solve for X. Geometry

Answer 1

x = 14

Explanation:

Look at the picture.

`m\widehat{BC}=2m\angle BDC\\\\m\widehat{BC}=2(x+25)\qquad\text{use the distributive property}\\\\m\widehat{BC}=(2)(x)+(2)(25)\\\\m\widehat{BC}=2x+50`

The whole circle is 360°. Therefore we have the equation:

`(10x+2)+(2x+50)+(10x)=360\\\\10x+2+2x+50+10x=360\qquad\text{combine like terms}\\\\(10x+2x+10x)+(2+50)=360\\\\22x+52=360\qquad\text{subtract 52 from both sides}\\\\22x+52-52=360-52\\\\22x=308\qquad\text{divide both sides by 52}\\\\(22x)/(22)=(308)/(22)\\\\x=14`

Answer 2

Check the picture below.

so we have the inscribed angle D intercepting the arcBC, so 2D = arcBC.

let's keep in mind that a circle has a total of 360°, so the arc in red there, is 360° minus the others.

`\bf \stackrel{2\measuredangle D}{2(x+25)}~~ = ~~\stackrel{\widehat{BC}}{360-(10x)-(10x+2)}\implies 2x+50=360-10x-10x-2 \\\\\\ 2x+50=358-20x\implies 22x+50=358\implies 22x=308 \\\\\\ x = \cfrac{308}{22}\implies x = 14`