Complete the proof....
1 answer:
Answer:
The correct options are;
1. Definition of supplementary angles
2. m∠1 + m∠2 = m∠1 + m∠3
3. m∠2 = m∠3
4. Definition of Congruent Angles
Step-by-step explanation:
The two column proof is presented as follows;
Statement Reason
1. ∠1 and ∠2 are supplementary Given
∠1 and ∠3 are supplementary
2. m∠1 + m∠2 = 180° Definition of supplementary angles
m∠1 + m∠3 = 180°
3. m∠1 + m∠2 = m∠1 + m∠3 Transitive Property
4. m∠2 = m∠3 Subtraction Property of Equality
5. ∠2 ≅ ∠3 Definition of Congruent Angles
Given that angles ∠1 and ∠2 are supplementary angles and angles ∠1 and ∠3 are are also supplementary angles, then the sums of m∠1 + m∠2 and m∠1 + m∠3 are equal, therefore, ∠2 and ∠3 have equal quantitative value and therefore ∠2 = ∠3 and by definition, ∠2 ≅ ∠3.
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Answer:
The number of free throws, two-point throw, and three-point throw are 135, 173, and 111 respectively.
Step-by-step explanation:
Let x,y, and z are the numbers of two-point field goals, numbers of three-point field goals, and the number of free-throws (one-point goal) respectively.
The total points= 814
As the number of two-point goals was 49 less than double the number of three-point field goals she made.
Again, the number of free goals was 38 less than the number of two-point field goals she made.
From equations (i) and (iii)
2x+3y+x-38=814
[using equation (ii)]
From equation (ii),
From equation (iii),
.
Hence,
The number of free throws, z= 135
The number of two-point throw, x=173
The number of three-point throw, y=111.