Answer:
The correct option is
a. Loana established all necessary conditions but then used an inappropriate congruence criterion
Step-by-step explanation:
The two column proof is presented as follows;
Statement 
Reason
1. PQ = RQ = 9 Given
2. m∠O = m∠S = 90° Given
3. m∠PQO = m∠RQS = 63° Given
4. ΔOPQ ≅ ΔSRQ Angle-Side-Angle Congruence
The given parameters shows that the side, adjacent angle, and next adjacent angle of triangle ΔOPQ are congruent to the corresponding side, adjacent angle, and next adjacent angle of triangle ΔSRQ, therefore, the appropriate congruency criterion that shows that ΔOPQ is congruence to ΔSRQ is the Side-Angle-Angle which is the same as the Angle-Angle-Side AAS, congruency criterion
Answer:
D 6
Step-by-step explanation:
1-2=-1 and the absolut value of -1 is 1
2--3=5
5+1=6
Since <em>l</em> and <em>m</em> are parallel, the unlabeled angle adjacent to the 63° one also has measure (7<em>x</em> - 31)° (it's a pair of alternating interior angles).
Then the three angles nearest line <em>m</em> are supplementary so that
(7<em>x</em> - 31)° + 63° + (5<em>x</em> - 8)° = 180°
Solve for <em>x</em> :
(7<em>x</em> - 31) + 63 + (5<em>x</em> - 8) = 180
12<em>x</em> + 24 = 180
12<em>x</em> = 156
<em>x</em> = 13
The bottom-most angle labeled with measure (4<em>y</em> + 27)° is supplementary to the angle directly adjacent to it, so this unlabeled angle has measure 180° - (4<em>y</em> + 27)° = (153 - 4<em>y</em>)°. The interior angles of any triangle have measures that sum to 180°, so we have
(7<em>x</em> - 31)° + 63° + (153 - 4<em>y</em>)° = 180°
We know that <em>x</em> = 13, so 7<em>x</em> - 31 = 60. Then this simplifies to
123° + (153 - 4<em>y</em>)° = 180°
Solve for <em>y</em> :
123 + (153 - 4<em>y</em>) = 180
276 - 4<em>y</em> = 180
96 = 4<em>y</em>
<em>y</em> = 24
Answer:
The answer is 0.15
Step-by-step explanation:
3 × 5 × (0.1) × (0.1)
15 × (0.01) = 0.15
Thus, The answer is 0.15
<u>-TheUnknownScientist 72</u>
