Congruent because both angles are the same
The first thing we must do for this case is to calculate the scale factor.
For this, we make the relationship between two parallel sides.
We have then:
Substituting values we have:
We are now looking for the value of AB
We have then:
Substituting values:
Answer:
The scale factor is:
The value of AB is:
The measure of the missing side of the right triangle are as follows;
adjacent side = 5√2
hypotenuse = 10
<h3 /><h3>How to find the side of a right triangle?</h3>
A right angle triangle has one of its angles as 90 degrees.
Therefore,
using trigonometric ratios,
tan 45 = opposite / adjacent
tan 45 = 5√2 / a
adjacent side = 5√2 / 1
Therefore,
adjacent side = 5√2
sin 45 = opposite / hypotenuse
hypotenuse = 5√2 / √2 / 2
hypotenuse = 5√2 × 2 / √2
hypotenuse = 10
learn more on right triangle here: brainly.com/question/6322314
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Option A:
∠TSU and ∠QPS are corresponding angles.
Solution:
Given OQ and RT are parallel lines.
To find which angles are corresponding angles.
Option A: ∠TSU and ∠QPS
They are on the same side of the parallel lines.
These are corresponding angles.
Option B: ∠OPS and ∠OPN
These are adjacent angles in a straight line.
It is not corresponding angles.
Option C: ∠RSP and ∠QPS
These are alternate interior angles.
It is not corresponding angles.
Option D: ∠OPN and ∠TSP
These are alternate angles.
It is not corresponding angles.
Hence ∠TSU and ∠QPS are corresponding angles.
Option A is the correct answer.
