All categories

3 years ago

Triangles PQR and XYZ are similar triangles. Which are the other two angle measures of triangle XYZ?

Mathematics

2 answers:

Julli [10]3 years ago

5 0

Angle Z = Angle R = 35 degrees

Angle Y = 180-70-35 = 180-105 = 75

35 & 75 degrees

Effectus [21]3 years ago

3 0

Answer:

A, C

Step-by-step explanation:

We are given that the triangles PQR and XYZ are similar.

Also, ∠ZXY = 70° and ∠PRQ = 35°.

Now, we know that when two triangles are similar, then the corresponding angles are same.

Therefore, ∠XZY = ∠PRQ = 35°

Now, in triangle XYZ, we have ∠XZY = 35° and ∠ZXY = 70°.

Since, we know that the sum of the angles of a triangle is 180°.

So, ∠XZY + ∠ZXY + ∠ZYX = 180°

i.e. 35° + 70° + ∠ZYX = 180°

i.e. ∠ZYX = 180° - ( 35° + 70° )

i.e. ∠ZYX = 180° - 105°

i.e. ∠ZYX = 75°

Hence, the other two angle measures of triangle XYZ are 35° and 75°.

You might be interested in

Amy is pulling a wagon with a force of 30 pounds up a hill at an angle of 25°. Give the force exerted on the wagon as a vector a

Fofino [41]

Answer:

Vector (ordered pair - rectangular form)

$\vec F = (27.189,12.679)\,[lbf]$

Vector (ordered pair - polar form)

$\vec F = (30\,lbf, 25^{\circ})$

Sum of vectorial components (linear combination)

$\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]$

Step-by-step explanation:

From statement we know that force exerted on the wagon has a magnitude of 30 pounds-force and an angle of 25° above the horizontal, which corresponds to the +x semiaxis, whereas the vertical is represented by the +y semiaxis.

The force ( $\vec F$ ), in pounds-force, can be modelled in two forms:

Vector (ordered pair - rectangular form)

$\vec F = \left(\|\vec F\|\cdot \cos \theta, \|\vec F\|\cdot \sin \theta\right)$ (1)

Vector (ordered pair - polar form)

$\vec F = \left(\|\vec F\|, \theta\right)$

Sum of vectorial components (linear combination)

$\vec {F} = \left(\|\vec F\|\cdot \cos \theta\right)\cdot \hat{i} + \left(\|\vec F\|\cdot \sin \theta \right)\cdot \hat{j}$ (2)

Where:

$\|\vec F\|$ - Norm of the vector force, in newtons.

$\theta$ - Direction of the vector force with regard to the horizontal, in sexagesimal degrees.

$\hat{i}$ , $\hat{j}$ - Orthogonal axes, no unit.

If we know that $\|\vec F\| = 30\,lbf$ and $\theta = 25^{\circ}$ , then the force exerted on the wagon is:

Vector (ordered pair - rectangular form)

$\vec F= \left(30\cdot \cos 25^{\circ}, 30\cdot \sin 25^{\circ}\right)\,[lbf]$

$\vec F = (27.189,12.679)\,[lbf]$

Vector (ordered pair - polar form)

$\vec F = (30\,lbf, 25^{\circ})$

Sum of vectorial components (linear combination)

$\vec F = (30\cdot \cos 25^{\circ})\cdot \hat{i} + (30\cdot \sin 25^{\circ})\cdot \hat{j}\,[N]$

$\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N]$

8 0

2 years ago

What tables could be used to verify that the functions they represent are inverses of each other? Select two options

algol13

Answer: B and E

Step-by-step explanation:

I just took the assignment. :)

5 0

2 years ago

Read 2 more answers

Is -6/5x=y proportional

yaroslaw [1]

Yes, It Is A Full Equation.

5 0

3 years ago

Read 2 more answers

Juno calculated the area of a square to be 4/9 square yard. Which shows the side length of the square?

Stella [2.4K]

$\bf \textit{area of a square}\\\\
A=s^2~~
\begin{cases}
s=side's~length\\
--------\\
A=\frac{4}{9}
\end{cases}\implies \cfrac{4}{9}=s^2
\\\\\\
\sqrt{\cfrac{4}{9}}=s\implies \cfrac{\sqrt{4}}{\sqrt{9}}=s\implies \cfrac{2}{3}=s$

3 0

3 years ago

To find 8 ×17, I double and halve

anastassius [24]

Answer:

what is the question?

Step-by-step explanation:

6 0

2 years ago