Answer:
A, C, D
Step-by-step explanation:
Consider triangles NKL and NML. These triangles are right triangles, because
In these right triangles:
- reflexive property;
- given
Thus, triangles NKL and NML by HA postulate. Congruent triangles have congruent corresponding parts, so
![\overline{KN}\cong \overline{NM}\\ \\\overline{KL}\cong \overline{LM}\ [\text{option D is true}]](https://tex.z-dn.net/?f=%5Coverline%7BKN%7D%5Ccong%20%5Coverline%7BNM%7D%5C%5C%20%5C%5C%5Coverline%7BKL%7D%5Ccong%20%5Coverline%7BLM%7D%5C%20%5B%5Ctext%7Boption%20D%20is%20true%7D%5D)
Since
then
![7x-4=5x+12\\ \\7x-5x=12+4\\ \\2x=16\\ \\x=8\ [\text{option A is true}]\\ \\MN=KN=7\cdot 8-4=56-4=52\ [\text{option C is true}]](https://tex.z-dn.net/?f=7x-4%3D5x%2B12%5C%5C%20%5C%5C7x-5x%3D12%2B4%5C%5C%20%5C%5C2x%3D16%5C%5C%20%5C%5Cx%3D8%5C%20%5B%5Ctext%7Boption%20A%20is%20true%7D%5D%5C%5C%20%5C%5CMN%3DKN%3D7%5Ccdot%208-4%3D56-4%3D52%5C%20%5B%5Ctext%7Boption%20C%20is%20true%7D%5D)
Option B is false, because KN=52 units.
Option E is false, because LN is congruent KN, not LM
Answer:
133°
Step-by-step explanation:
As vertically opposite angles are equal,
< B E D = < F E G
Therefore,
< B E D = 47°
We know that co - interior angles which occur between 2 parallel lines, are added up to 180°.
Given that, < A B E = x
Therefore,
< B E D + < A B E = 180 °
47 + x = 180
x = 180 - 47
x = 133°
Let me know if you have any other questions. :)
Answer:
The correct option is;
45°
Step-by-step explanation:
By angle sum theorem, we have that the sum of angles in a triangle = 180°
Therefore, we have;
When the interior angles of the triangle are constructed to be 60° and 75°, we have by the angle sum theorem;
The third angle + 60° + 75° = 180°
Which gives;
The third angle = 180°- 60° - 75° = 180°- 135° = 45°
The measurement of the third angle by the angle sum theorem will be 45°
The correct option is ∠third angle = 45°.
The Alternate Interior Angles theorem states, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. A theorem is a proven statement or an accepted idea that has been shown to be true.
$69 ÷ 6 = 11.5 per DVD
11.5 × 4 = 46
