Please help! It’s for a test, I’ll also give brainliest!
2 answers:
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<u>EXPLANATION</u><u>:</u>
In ∆ ABC , ∠ABC = 40°
- ∠CAB = x°
- & ∠ACD = 50°
∠ACD is an exterior angle formed by extending BC to D
We know that
The exterior angle of a triangle formed by extending one side is equal to the sum of the opposite interior angles.
∠ACD = ∠CAB + ∠ABC
⇛50° = x° + 40°
⇛x° = 50°-40°
<h3>⇛x° = 10°</h3>and
In ∆ ACD , AC = CD
⇛ ∠CDA = ∠CAD
Since the angles opposite to equal sides are equal.
Let ∠CDA = ∠CAD = A°
We know that
The sum of all angles in a triangle is 180°
In ∆ ACD,
∠CDA +∠CAD + ∠ACD = 180°
A°+A°+50° = 180°
⇛2A°+50° = 180°
⇛2A° = 180°-50°
⇛2A° = 130°
⇛A° = 130°/2
⇛A° = 65°
now,
∠CDA = ∠CAD = 65°
∠BAC + ∠CAD+y = 180°
Since angles in the same line
10°+65°+y = 180°
⇛75°+y =180°
⇛y = 180°-75°
<h3>⇛y = 105°</h3><u>Answer</u><u>:</u> Hence, the value of “x” & “y” will be 10° and 105° respectively.
Answer:
B. 199
Step-by-step explanation:
We are given an Arithmetic sequence : 3, 7, 11, 15, ...
We are supposed to find the 50th term .
So, first consider the formula of nth term in Arithmetic mean:
where
a is first term of sequence
n is term position
d is common difference
= the term you are supposed to find
Now,
a = 3 ( first term )
n = 50 th term ( given )
d = 7-3 = 11-7 = 4(common difference
Substitute these value in the formula given above
⇒
⇒
⇒
⇒
Hence ,The 50th term of given arithmetic sequence is 199
So, OPTION B is correct .