Question

determining interior and exterior angles in circles
given:
in circle o,

• ( mwidehat{dj} = 150.9^circ )
• ( mwidehat{jc} = 37.4^circ )

use the interactive diagram to determine ( mangle dlj ).
the ( mangle dlj ) is (square) degrees
reason:

Explanation:

Step1: Recall the formula for an angle formed by a tangent and a secant

The measure of an angle formed by a tangent and a secant outside a circle is half the difference of the measures of the intercepted arcs. The formula is \( m\angle DLJ=\frac{1}{2}(m\widehat{DJ}-m\widehat{JC}) \).

Step2: Substitute the given values

We know that \( m\widehat{DJ} = 150.9^\circ \) and \( m\widehat{JC}=37.4^\circ \). Substitute these values into the formula:
\[

$$\begin{align*} m\angle DLJ&=\frac{1}{2}(150.9^\circ - 37.4^\circ)\\ &=\frac{1}{2}(113.5^\circ)\\ & = 56.75^\circ \end{align*}$$

\]

Answer:

\( 56.75 \)