Question

circle o with diameter ne and inscribed angle nte is shown. complete the steps to prove ∠nte is a right angle. enter your answers in the boxes. statements reasons 1. circle o has diameter ne and inscribed angle nte. given 2. $widehat{nse}$ is a semicircle. diameter divides a circle into 2 semicircles. 3. circle o measures 360°. measure of a circle is 360°. 4. $mwidehat{nse}=square$ degrees definition of semicircle 5. $mangle nte = 90^{circ}$ the measure of an inscribed angle is $square$ times the measure of its intercepted arc. 6. $angle nte$ is a right angle definition of right angle

Explanation:

Step1: Recall the measure of a semi - circle

A semi - circle is half of a circle. Since the measure of a full circle is 360°, the measure of a semi - circle is $\frac{360^{\circ}}{2}=180^{\circ}$. So, $m\overparen{NSE}=180$ degrees.

Step2: Recall the inscribed - angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc. Here, the inscribed angle $\angle NTE$ intercepts the semi - circle $\overparen{NSE}$ which has a measure of 180°. So, $m\angle NTE=\frac{1}{2}\times m\overparen{NSE}$. Since $m\overparen{NSE} = 180^{\circ}$, then $m\angle NTE=\frac{1}{2}\times180^{\circ}=90^{\circ}$.

Answer:

1. 180
2. $\frac{1}{2}$