Question

if m minor arc ML = 44 degrees and m arc DR = 136 degrees, find m angle T

Answer 1

To find the measure of angle \( T \) formed by two chords in a circle that subtend the given arcs, we can use the following relationships:

1. The measure of an angle formed by two chords that intersect inside a circle (let's say angle \( T \)) is equal to half the sum of the measures of the arcs intercepted by the angle.

For angle \( T \), we need to identify the arcs involved. Assuming \( ML \) and \( DR \) are arcs that subtend angle \( T \):

- \( ML \) (minor arc) measures \( 44^\circ \).
- \( DR \) (arc opposite to \( ML \)) measures \( 136^\circ \).

Now, plug in these values into the angle formula:

\[
m \angle T = \frac{1}{2} \left( m \text{ arc } ML + m \text{ arc } DR \right)
\]

\[
m \angle T = \frac{1}{2} \left( 44^\circ + 136^\circ \right)
\]

\[
m \angle T = \frac{1}{2} \left( 180^\circ \right)
\]

\[
m \angle T = 90^\circ
\]

Thus, the measure of angle \( T \) is \( 90^\circ \).