Answer:
69°, 69°, and 42°
Step-by-step explanation:
Isosceles triangles have three angles -- one vertex angle and two base angles.
The <u>base angles have the same measure</u> and the vertex angle has a different measure.
<u>Remember all triangles' interior angles sum to 180°.</u>
If the vertex angle is 42°, then the two base angles combined are:
180° - 42° = 138°
Since the base angles are the same, <u>each base angle is:</u>
138° ÷ 2 = 69°
Therefore the angles in the triangle measure 69°, 69°, and 42°.
Answer:
Step-by-step explanation:
Grace paid $4.80/(4 notebooks) = {$4.80/4)/notebook = $1.20 per notebook
Jim paid $3.90/(3 notebooks) = ($3.90/3)/notebook = $1.30 per notebook
Grace found the better buy.
Answer:
z=125
y=30
Step-by-step explanation:
x and z are the same because of the congruent sides then is triangle sum
Triangular sequence = n(n + 1)/2
If 630 is a triangular number, then:
n(n + 1)/2 = 630
Then n should be a positive whole number if 630 is a triangular number.
n(n + 1)/2 = 630
n(n + 1) = 2*630
n(n + 1) = 1260
n² + n = 1260
n² + n - 1260 = 0
By trial an error note that 1260 = 35 * 36
n² + n - 1260 = 0
Replace n with 36n - 35n
n² + 36n - 35n - 1260 = 0
n(n + 36) - 35(n + 36) = 0
(n + 36)(n - 35) = 0
n + 36 = 0 or n - 35 = 0
n = 0 - 36, or n = 0 + 35
n = -36, or 35
n can not be negative.
n = 35 is valid.
Since n is a positive whole number, that means 630 is a triangular number.
So the answer is True.
