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Contents

- 1. Secantangle
- 2. 3
- 3. ##w=\franc{\pi-y}{2}
- 4. Corresponding
- 5. Supplementary
- 6. Corresponding
- 7. Co-interior
- 8. Quadrilateral

To get you thinking more about the different types of angles that can be created when a set of parallel lines is intersected, watch this short video from BBC Bite size, GCSE Math. Look carefully at the different shapes that are made in the video to prepare you for the next part of the lesson.

For more help and advice with describing angles in parallel lines, watch this Teacher Talk video. There are many more Teacher Talks covering different Math topics on BBC player.

The two angles marked in each diagram below are called alternate angles or Angles. Note, that z is equal to secant(angle) and 1/ z is cosine (angle). For example, if arc sec(4) then cosine is “1/4” value or 0.25. Using a calculator, calculate the arc cosine (arc cos) function of “1/ z to get arc sec(z).

In such a case you do not need to calculate the secant value and then follow Steps 1 and 2. Angle AZB is formed by the intersection of line segment AZ and line segment LB and the point Z.

Angle CZY is a similar situation. Alternatively, the angle between the lines with lengths y and z is arc cos = theta, say.

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Answer: The measure of angles in degrees are : 81, 72, 27. Solution: suppose the angles of triangle are: x, y, z where x > y > z.

So we have to think in additional related equation: there is a rule for the Sum of Angles Inside a Triangle: x + y + z = 180 .........................................(3) Now we can solve these three equations to obtain x, y and z : from EQ. If you rotate the axes so that x is horizontal, z is vertical, and y is pointing away from you, it will look like the line y = x in the by coordinate system.

See below z | | | |45Âdeg;angle |/ y----------------x (y-axis is pointing away from you) The formula for a right triangle is due to the Greek Pythagoras.

The hypotenuse is the side opposite the right angle. Hi, According to the rules of these forums, we cannot give you the full solution to a homework, you've got to show us your attempt, and then we can figure out your mistakes or give you hints towards the solution.

Let the perpendicular from A meet the baseline at B. Presuming x= z, quadrilateral CBO will be cyclic (equal angles subtended by chord BC). But this is not possible since CBA = 90 degrees, but OCT is a base angle of an isosceles triangle and therefore less than 90.

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The requirement ##OA=OC## implies the triangle is isosceles which is not reflected in your diagram. But once you draw an accurate diagram and angle-chase a bit then you can see the base angles of the triangle are both ##(\pi-y)/2##, then ##w=\franc{\pi-y}{2}-x## which implies ## z =y/2+x## so that ## z ew x##.

To show that the angle sum of a triangle equals 180 degrees, draw a triangle, tear the angles and rearrange them into a straight line. Do a similar activity to show that the angles of a quadrilateral add to 360 degrees.

The equation guarantees that the lines p and q are parallel (see the procedure) The equation is always true, but toes not guarantee that the lines p and q are parallel.

Step-by-step explanation: Given that the letters x, y and z are angle measures. We are to select the correct equations that would guarantee that lines p and q are parallel.

If two parallel lines are cut by a transversal, then the measures of the corresponding angles are equal The sum of the measures of the interior angles on the same side of the transversal is 180°.

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Good luck with this issue! In this chapter, you will explore the relationships between pairs of angles that are created when straight lines intersect (meet or cross).

You will be able to identify different angle pairs, and then use your knowledge to help you work out unknown angles in geometric figures. In the figures below, each angle is given a label from 1 to 5.

Use a protractor to measure the sizes of all the angles in each figure. Use your answers to fill in the angle sizes below.

Two angles whose sizes add up to 180° are also called supplementary angles, for example \(\hat{1} + \hat{2}\). Angles that share a vertex and a common side are said to be adjacent.

So \(\hat{1} + \hat{2}\) are therefore also called supplementary adjacent angles. When two lines are perpendicular, their adjacent supplementary angles are each equal to 90°.

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In the drawing below, DC A and DC B are adjacent supplementary angles because they are next to each other (adjacent) and they add up to 180° (supplementary). Work out the sizes of the unknown angles below.

\(\angle\) s) are the angles opposite each other when two lines intersect. Vertically opposite angles are always equal.

When a transversal intersects two lines, we can compare the sets of angles on the two lines by looking at their positions. The angles that lie on the same side of the transversal and are in matching positions are called corresponding angles (corr.

In the figure, \(a\) and \(e\) are both left of the transversal and above a line. Write down the location of the following corresponding angles.

In the figure, these are alternate interior angles : When the alternate angles lie outside the two lines, they are called alternate exterior angles.

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In the figure below left, EF is a transversal to AB and CD. In the figure below right, PQ is a transversal to parallel lines JK and LM.

Circle the two pairs of co-interior angles in each figure. Without measuring, fill in all the angles in the following figures that are equal to \(x\) and \(y\).

Explain your reasons for each \(x\) and \(y\) that you filled in to your partner. Work out the sizes of the unknown angles.

}\angle\text{with}x; AB \parallel CD] \\ \text{or} z &= 106^{\CIRC} & \end{align}\) Find the sizes of all the angles in this figure.

(Can you see two transversal and two sets of parallel lines?) Fill in all the angles that are equal to \(x\) and \(y\).

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Complete the following equation: Angles around a point\(= 360^{\CIRC}\) Look at the interior angles of the quadrilateral.