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Anna35 [415]
3 years ago
13

The figure below shows a straight line AB intersected by another straight line t:

Mathematics
1 answer:
BaLLatris [955]3 years ago
4 0

When two straight lines intersect, the pairs of nonadjacent angles in opposite posi-tions are known as vertical angles.

If a segment AB is intersected by a transversal labeled t, then ∠1 and ∠3 and ∠2 and ∠4 are vertically angles formed by the transversal t on the segment AB.

Angles ∠1 and ∠2 can be described as adjacent and supplementary angles, so

m\angle 1+m\angle 2=180^{\circ}.

Angles ∠3 and ∠2 can be also described as adjacent and supplementary angles, so

m\angle 3+m\angle 2=180^{\circ}.

Subtract from the first equation the second equation:

m\angle 1+m\angle 2-(m\angle 3+m\angle 2)=180^{\circ}-180^{\circ},\\ m\angle 1-m\angle 3=0,\\ m\angle 1=m\angle 3.

Similarly you can prove that m\angle 2=m\angle 4.

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Line segment TS is tangent to circle O at point N.
garik1379 [7]

Answer:

  148°

Step-by-step explanation:

The measure of the intercepted arc QN is twice the measure of inscribed angle QNT.

  arc QN = 2(74°) = 148°

_____

<em>Comment on the question and answer</em>

Your description "on the circle between points Q and N" is ambiguous. You used the same description for both points P and R. The interpretation we used is shown in the attachment. If point P is on the long arc NQ, then the measure of arc QPN will be the difference between 148° and 360°, hence 212°. You need to choose the answer that matches the diagram you have.

__

We call angle QNT an "inscribed angle" because it is a degenerate case of an inscribed angle. The usual case has the vertex of the angle separate from the ends of the arc it intercepts. In the case of a tangent meeting a chord, the vertex is coincident with one of the ends of the intercepted arc. The relation between angle measure and arc measure remains the same: 1 : 2.

7 0
3 years ago
Please help me with this :)))
Juliette [100K]

Answer:

Transitive

Step-by-step explanation:

3 0
2 years ago
The earth travels one full rotation around the sun in approximately 365.25 days. How many minutes does it take for the earth to
kozerog [31]

Step-by-step explanation:

365.25days

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365.25days= 365.25×1440

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8 0
2 years ago
Part A:
Soloha48 [4]

Answer:

Option D

Step-by-step explanation:

A). From the graph attached,

    Arrow AB represents the RISE and arrow BC represents the RUN.

B). RUN from point A to B (Horizontal distance) = 2 units

    Rise from point A to B (Vertical distance) = -4 [Since, downwards arrow represents negative notation]

    Slope of the line segment AB = \frac{\text{Rise}}{\text{Run}}

                                                       = \frac{-4}{2}

                                                       = -2

   Therefore, slope of the line = slope of the line segment AB = -2

    Option D will be the correct option.

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3 years ago
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hodyreva [135]
I will help you with your problem
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