Question

What is the value of x in the circle below?80°2°.120°40°80°100°120°

Answer 1

Let us start by sketching out the image

To solve fo x, we are going to solve for y first using the Intersecting chord theorem.

$y^0=\frac{1}{2}(AB+CD)$

Given that,

$\begin{gathered} AB=80^0 \\ CD=120^0 \end{gathered}$

Therefore,

$\begin{gathered} y^0=\frac{1}{2}(80^0+120^0) \\ y^0=\frac{1}{2}(200^0)=100^0 \\ y^0=100^0 \end{gathered}$

Solving for x,

$x^0+y^0=180^0(sumofanglesonastraightlineis180^o)$$\begin{gathered} x^0+100^0=180^0 \\ x^0=180^0-100^0 \\ x^0=80^0 \end{gathered}$

Hence, x° = 80°.

The correct option is option 2.