Answer:
1. 30°
2.90°
3. 12 units
Step-by-step explanation:
I can't believe there's nothing confirming that this is a parallelogram/a rhombus?! Assuming is awful, and I wish you could say you can't know for sure lol but for the sake of this answer, let's just call it a rhombus. (There was probably some context elsewhere that you didn't put over here, hopefully.)
1.
The reason I say this is: in a rhombus, the diagonals bisect the angles. This means that the diagonals split the angles they meet into two equal parts. That way, it would make sense. m∠QPR=m∠SPR=30°.
2.
If it is a rhombus, the diagonals are perpendicular to each other, so m∠QTP should be 90°.
3.
Diagnonals in a rhombus (and in any parallelogram) bisect each other, so PT=TR=6, and RP=PT+TR=12 units.
Sorry if this is all dreadfully wrong, and I hope I helped you!
Answer:
Base angle = 72
Vertex angle = 18
Step-by-step explanation:
Measure of the base angle = x. But there are two of them. (Definition of isosceles). Keep that in mind.
The vertex angle is 1/4 of one of the base angles. That means that the vertex is 1/4 x
All three angles = 180 degrees.
So we have x + x + x/4 = 180 degrees.
change 1/4x to 0.25x x since 1/4 = 0.25
Equation
x + x + 0.25 = 180
2.5x = 180
Solution
2.5x = 180 Divide by 2.5 on both sides
2.5x/2.5 = 180/2.5
x = 72
Answer
That means that each base angle = 72 degrees
The Vertex Angle = 72/4 = 18
Answer:
We have sinθ = 12/13
The method here is to figure out the value of θ
Using a calculator sin^(-1)(12/13) =67.38°
67.38° is in quadrant 1 so we must substract 67.38° from 180° wich is π
- 180-67.38= 112.61° ⇒ θ= 112.61°
Now time to calculate cos2θ and cosθ using a calculator
- cosθ = -5/13
- cos2θ = -0.7
The values we got make sense since θ is in quadrant 2 and 2θ in quadrant 3
