Answer:
The value of ∠A is 62° ⇒ c
The value of ∠B is 54°⇒ d
Step-by-step explanation:
<em>In a triangle, the measure of an exterior angle at a vertex of the triangle equals the sum of the measures of the two opposite interior angles to this vertex.</em>
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In Δ ABC
∵ The measure of the exterior angle at the vertex C = 116°
∵ The opposite interior angles to vertex C are ∠A and ∠B
∵ m∠A = (3x - 13)°
∵ m∠B = (2x + 4)°
→ By using the rule above
∴ (3x - 13) + (2x + 4) = 116
→ Add the like terms in the left side
∵ (3x + 2x) + (-13 + 4) = 116
∴ 5x + -9 = 116
∴ 5x - 9 = 116
→ Add 9 to both sides
∵ 5x - 9 + 9 = 116 + 9
∴ 5x = 125
→ Divide both sides by 5
∴ x = 25
→ To find the measures of angle A and B substitute x in their
measures by 25
∵ m∠A = 3(25) - 13 = 75 - 13
∴ m∠A = 62°
∴ The value of ∠A is 62°
∵ m∠B = 2(25) + 4 = 50 + 4
∴ m∠B = 54°
∴ The value of ∠B is 54°
Answer:
See below
Step-by-step explanation:
Distance = rate * time
= 65 m/hr * 2 1/4 hr = 146.25 miles
rate = distance / time
for Declan : rate = 146.25 miles / (2 hrs + 35/60 min) = 56.61 mph
Step-by-step explanation:
Mid Point : A point which lies on the line segment and is equidistant from both the ends of the segment is called a mid point.
A line segment can have ONLY ONE mid point and it divides the line segment into two equal parts.
Now, Given : C is the midpoint of AB.
and B is the midpoint of CD.
⇒ AC = BC and BC = BD
Now by Euclid's Lemma
- "Things which are equal to the same thing are equal to each other."
Here, AC = BC , and BC = BD
⇒ AC = BD
Hence the result.
Answer:
$0.75
Step-by-step explanation:
We have been given that Yuki bought a pound of confetti for $12.
To find the price of per ounce of confetti, we will divide the total price of 1 pound confetti by number of ounces in 1 pound.
1 pound = 16 ounces.
Let us divide 12 by 16 to find the price of confetti per ounce.
Therefore, the price of per ounce confetti is $0.75.
