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:

• $m\mathrm{\angle }AB={54}^{\circ }$
• $m\mathrm{\angle }BC={115}^{\circ }$
• $m\mathrm{\angle }CD={86}^{\circ }$

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

1. Calculate $m\mathrm{\angle }AD$:

   Since: $$m\mathrm{\angle }AB+m\mathrm{\angle }CD={180}^{\circ }$$

   Plugging in the known values: $${54}^{\circ }+m\mathrm{\angle }CD={180}^{\circ }$$ $$m\mathrm{\angle }CD={180}^{\circ }-{54}^{\circ }={126}^{\circ }$$

   Next, we can find $m\mathrm{\angle }AD$: $$m\mathrm{\angle }BC+m\mathrm{\angle }AD={180}^{\circ }$$

   So: $${115}^{\circ }+m\mathrm{\angle }AD={180}^{\circ }$$ $$m\mathrm{\angle }AD={180}^{\circ }-{115}^{\circ }={65}^{\circ }$$

Now we can check the statements provided:

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