Answer :
Sure! Let's solve each part of the question step by step.
7. Complementary Angles:
We know that complementary angles add up to 90 degrees. In the problem, it states that angle [tex]\(A\)[/tex] and angle [tex]\(B\)[/tex] are complementary, and it gives us [tex]\(m \angle A = x\)[/tex]. Since [tex]\(A + B = 90\)[/tex], we can find angle [tex]\(B\)[/tex] by rearranging the equation:
[tex]\[ m \angle B = 90 - x \][/tex]
So, the correct answer would be:
D. [tex]\(90 - x\)[/tex]
8. Geometric Proof Angle Relationship:
For this question, we need to identify the angle relationship that can be used alone to justify that two angles are congruent. The property that directly establishes congruency of angles without needing additional conditions is:
Vertical angles are always congruent.
Therefore, the answer is:
Q. vertical angles
9. Measure of the Largest Angle in the Triangle:
For this part, it seems we're given an expression [tex]\(2x + 1 + x + 15\)[/tex] as the measure of one of the angles in a triangle. Let's break down the expression:
1. Combine the like terms:
[tex]\[ 2x + x + 1 + 15 = 3x + 16 \][/tex]
To find the measure of this angle, let's assume that [tex]\(x\)[/tex] is given as 15 from the problem, and substitute [tex]\(x = 15\)[/tex] into the expression:
[tex]\[3(15) + 16 = 45 + 16 = 61\][/tex]
This would be the measure of the angle using given conditions. However, it seems we should compare this to a list of potential answers. Therefore, if a mistake was made and you were seeking to determine from these choices, double checking is advised:
Since none of the given choices [tex]\(41, 46.5, 56, 83\)[/tex] exactly match that angle measure, it would be prudent to revisit all conditions where necessary, unless scope was misunderstood.
If there is cleared data and values provided in full match, adjusting values or confirming possibilities should be demonstrated - it would be appropriate contextually only by clear comprehension of all question factors.
7. Complementary Angles:
We know that complementary angles add up to 90 degrees. In the problem, it states that angle [tex]\(A\)[/tex] and angle [tex]\(B\)[/tex] are complementary, and it gives us [tex]\(m \angle A = x\)[/tex]. Since [tex]\(A + B = 90\)[/tex], we can find angle [tex]\(B\)[/tex] by rearranging the equation:
[tex]\[ m \angle B = 90 - x \][/tex]
So, the correct answer would be:
D. [tex]\(90 - x\)[/tex]
8. Geometric Proof Angle Relationship:
For this question, we need to identify the angle relationship that can be used alone to justify that two angles are congruent. The property that directly establishes congruency of angles without needing additional conditions is:
Vertical angles are always congruent.
Therefore, the answer is:
Q. vertical angles
9. Measure of the Largest Angle in the Triangle:
For this part, it seems we're given an expression [tex]\(2x + 1 + x + 15\)[/tex] as the measure of one of the angles in a triangle. Let's break down the expression:
1. Combine the like terms:
[tex]\[ 2x + x + 1 + 15 = 3x + 16 \][/tex]
To find the measure of this angle, let's assume that [tex]\(x\)[/tex] is given as 15 from the problem, and substitute [tex]\(x = 15\)[/tex] into the expression:
[tex]\[3(15) + 16 = 45 + 16 = 61\][/tex]
This would be the measure of the angle using given conditions. However, it seems we should compare this to a list of potential answers. Therefore, if a mistake was made and you were seeking to determine from these choices, double checking is advised:
Since none of the given choices [tex]\(41, 46.5, 56, 83\)[/tex] exactly match that angle measure, it would be prudent to revisit all conditions where necessary, unless scope was misunderstood.
If there is cleared data and values provided in full match, adjusting values or confirming possibilities should be demonstrated - it would be appropriate contextually only by clear comprehension of all question factors.