For the triangles to be congruent by HL, what must be the value of x?
1 answer:
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Answer:
Step-by-step explanation:
<h3><u>Given that:</u></h3>Exterior angle of L = 5x + 12
M = 3x - 2
N = 50
<h3><u>Statement:</u></h3>- Exterior angle is equal to the sum of non-adjacent interior angles.
So, the exterior angle that is adjacent to L is equal to the sum of non-adjacent sides (M and N) of the triangle.
Here,
Exterior angle of L = M + N
5x + 12 = 3x - 2 + 50
5x + 12 = 3x + 48
Subtract 12 to both sides
5x = 3x + 48 - 12
5x - 3x = 36
2x = 36
Divide 2 to both sides
x = 18
So,
<h3><u>Measure of angle M:</u></h3>= 3x - 2
= 3 (18) - 2
= 54 - 2
= 52°
Now,
<h3><u>Measure of angle L:</u></h3><u>We know that,</u>
- Sum of all the interior angles of triangle is 180 degrees.
L + M + N = 180°
L + 52 + 50 = 180
L + 102 = 180
Subtract 102 to both sides
L = 180 - 102
L = 78°
Answer: The correct option is (D) 196608.
Step-by-step explanation: We are given to find the value of the 9th term in the following geometric sequence :
3, 12, 48, 192, . . .
We know that
the n-th term of a geometric sequence with first term a and common ratio r is given by
For the given sequence, we have
first term, a = 3 and the common ratio, r is given by
Therefore, the 9th term of the given sequence will be
Thus, the required 9th term of the given sequence is 196608.
Option (D) is CORRECT.