do you remember what is special about the interior angles of a triangle they always add up to 180 degrees and whenever you use this fact you need to give the following reason if a triangle has no equal sides we call it a scalene triangle please note the angles are also all different in a scalene triangle do you remember what we call a triangle with two equal sides it is called an isosceles triangle this triangle also has two equal angles which lie at the ends of the equal sides or opposite to the equal sides do you remember the name of the triangle with three equal sides it is an equilateral triangle this triangle also has three equal angles and because the angles of a triangle always add up to 180 degrees each angle is 60 degrees and what type of triangle is this triangle it is a right-angled triangle this angle is 90 degrees which is of course the right angle and the side opposite this angle is called the hypotenuse please pause to study this important information do you remember what type of angle we get when we extend a side of a triangle we get an exterior angle of the triangle these two angles are called the opposite interior angles an important fact to remember here is that the exterior angle is always equal to the sum of the opposite interior angles and whenever you use this fact you need to write the following reason please pause to study this information let's now use our knowledge of triangles together with vertically opposite angles and parallel lines to answer a few problems or riders if you can't remember all of this we suggest you first listen to the previous grade nine lessons and maybe some grade eight lessons on this topic here is the first problem or rider please pause to read it to find X we can use triangle ABC together with its exterior angle 2x as we have said 2x is an exterior angle and this is equal to the sum of the opposite interior angles 50 degrees and X plus 10 degrees and don't forget to write the reason in the step to solve this equation we begin by adding 50 degrees to ten degrees on the right we then subtract X from both sides X is therefore equal to 60 degrees the exterior angle is therefore two times sixty degrees or 120 degrees to find why we need to use this triangle and because it is an isosceles triangle Anglesey ad is also equal to y don't forget to write the reason in the step we can therefore write that y plus y plus 120 degrees equals 180 degrees y because the sum of the interior angles of a triangle is always 180 degrees to solve the equation we begin by adding like terms on the left we then subtract 100 20 degrees from both sides and then we divide both sides by 2y is therefore equal to 30 degrees please pause to check my working [Music] here is the next question please pause to read it we begin with the parallel lines and the letter F this means that angle Dec equals 90 degrees why because we have corresponding angles and a B is parallel to de we can now use triangle Dec can you see how we can use the fact that the angles of a triangle add up to 180 degrees to solve the equation we begin by collecting like terms on the left we then subtract 80 degrees from both sides and then we divide both sides by five X is therefore equal to 20 degrees to find why we again use parallel lines and the letter F this means that Y is equal to 3x minus 10 degrees and don't forget to write the reason we have just seen that X is 20 degrees so we can substitute 20 degrees in place of X here three times 20 degrees equals 60 degrees and sixty degrees minus ten degrees equals fifty degrees so Y is equal to 50 degrees please pause to check my working here is the next question please pause to read it we begin by using the parallel lines and the letter Z or n this means that 3x minus 24 degrees equals 2x y because there are alternate angles and a B is parallel to de to solve the equation we begin by subtracting 2x from both sides we then add 24 degrees to both sides X is therefore equal to 24 degrees before we can find why we first need to use these straight lines and the fact that vertically opposite angles are equal angle c1 is therefore equal to 57 degrees we are now ready to use triangle ABC because Y is the only unknown interior angle we are given that angle a is equal to 3x minus 24 degrees and we have just calculated that X is 24 degrees so to find angle a we need to substitute 24 degrees in place of X angle a is therefore equal to 48 degrees this means we can write the following equation because the angles of a triangle always add up to 180 degrees to solve the equation we begin by adding 48 degrees and 57 degrees on the left we then subtract 105 degrees from both sides why is therefore equal to 75 degrees please pause to check my working let's end with this question please pause to read it to find X is easy we just need to use triangle ABC and angle c 1 is of course 90 degrees we can therefore write the following equation and don't forget the reason to solve the equation we begin by adding 38 degrees and 90 degrees we then subtract 128 degrees from both sides X is therefore equal to 52 degrees to find why you need to recognize that triangle BCD is an isosceles triangle this means that angle c 2 and y are equal can you see a way of finding the size of angle c 2 let me help you we need to use parallel lines as well as the letter Z or n now can you see how to find angle C to yes angle Z 2 is equal to 52 degrees because alternate angles are equal and a B is parallel to CD this means that y is also equal to 52 degrees and the reason is isosceles triangle BCD and lastly to find Zed we need to use the fact that we have a straight line here this means that z+ 52 degrees + 52 degrees equals 180 degrees and the reason is angles on a straight line which are supplementary angles to solve the equation we begin by adding 52 degrees and 52 degrees on the left we then subtract 104 degrees from both sides Z is therefore equal to 76 degrees this completes the lesson good luck with the test