Answer:
a. 35 degrees
b. 145 degrees
Step-by-step explanation:
a. Since the two base angles of this triangle are congruent, we can conclude that the triangle is <em>isosceles, </em>which means that the two base angles and sides are congruent.
Now, knowing that information, we can subtract 110 from 180 (the sum of all interior angles in a triangle) and we get 70. But this isn't our answer. This is the sum of both base angles. Since the base angles are congruent, we can divide the 70 by 2 to get the measure of ONE base angle, which is 35 degrees.
b. There are two approaches to solve this problem. I have worked both out.
1) We can use the Exterior Angle Theorem, which states that the sum of the interior angles is equal to the exterior angle. We can add 110 to 35, so we get 145 degrees as the measure of <1.
2) The second approach is supplementary angles. Since we see that one of the base angles and <1 is on the same line, we can subtract 35 from 180 to find the measure of <1 to get 145 degrees.
Either way you use, you get the correct answer. Hope this helped!
Answer:
56
Step-by-step explanation:
The median is the middle number of a sorted set from least to greatest. After sorting the set 61, 48, 52, 65, 56, 77, 54 the set is 48, 52, 54, 56, 61, 65, 77.
The middle number in this set is 56 so the median is 56
Answer:
The value could replace q is 108 - n ⇒ the last answer
Step-by-step explanation:
* Lets study the values of quarters and nickles
- One quarter = 25 cents
- One nickle = 5 cents
- The number of coins is 108
- The coins are nickles or quarters only
- The coins worth $ 21
* Lets solve the problem
∵ The number of coins is 108 coins
- Let the quarter is q and the nickel is n
∴ q + n = 108 ⇒ (1)
∵ The coins worth $21
∵ $ 1 = 100 cents
∴ $21 = 21 × 100 = 2100 cents
∵ The quarter = 25 cents
∵ The nickels = 5 cents
∴ 25q + 5n = 2100 ⇒ (2)
- To find the value which replace q use equation (1)
∵ q + n = 108 ⇒ subtract n from both sides
∴ q = 108 - n
* The value could replace q is 108 - n
