Draw the following diagram: quadrilateral

Question

ABCD inscribed in circle
E. The mAB = 54°, mBC = 115°
, and
mCD = 86°.
. Select the true
statement. (1 point)
0 mLB = 95.5°
0 mADC = 84.5°
O mAD = 115°
OmLD = 169°

Answer 1

Given quadrilateral \(ABCD\) inscribed in circle \(E\), and the measures of the angles are:

• \(m \angle AB = 54^\circ\)
• \(m \angle BC = 115^\circ\)
• \(m \angle CD = 86^\circ\)

To find \(m \angle AD\), we can use the fact that the opposite angles of cyclic quadrilaterals sum to \(180^\circ\).

1. Calculate \(m \angle AD\):

   Since: \[ m \angle AB + m \angle CD = 180^\circ \]

   Plugging in the known values: \[ 54^\circ + m \angle CD = 180^\circ \] \[ m \angle CD = 180^\circ - 54^\circ = 126^\circ \]

   Next, we can find \(m \angle AD\): \[ m \angle BC + m \angle AD = 180^\circ \]

   So: \[ 115^\circ + m \angle AD = 180^\circ \] \[ m \angle AD = 180^\circ - 115^\circ = 65^\circ \]

Now we can check the statements provided:

1. \(m \angle B = 95.5^\circ\) - This cannot be true as \(m \angle B = 54^\circ\).
2. \(m \angle ADC = 84.5^\circ\) - This is incorrect as the opposite angle \(m \angle AD = 65^\circ\).
3. \(m \angle AD = 115^\circ\) - This is incorrect as we calculated \(m \angle AD = 65^\circ\).
4. \(m \angle LD = 169^\circ\) - \(LD\) seems to be a typographical error, assuming you meant \(m \angle AD\) still renders this incorrect.

None of the statements are true based on the calculations performed above. If the statements need clarification or there's more context, please provide that, and I'll help further!