ANGLES ON A STRAIGHT LINE ADD UP TO 180° 25/02/2019 ANGLES ON A STRAIGHT LINE ADD UP TO 180°

Angles on a straight line add up to 180 25/02/2019 Angles on a straight line add up to 180 a b a + b = 180° because there are 180° in a half turn.

25/02/2019 Examples x b 70o 35o Angle x = 180 – 35 = 145o Angle b = 180 – 70 = 110o Angle x = 180 – 35 = 145o

Task Find the size of the missing angles 25/02/2019 Task Find the size of the missing angles x 47o 1 114o y 2 3 4 76o a 82o b Angle x = 180 – 47 = 133o Angle y = 180 – 114 = 66o Angle a = 180 – 76 = 104o Angle b = 180 – 82 = 98o

25/02/2019 43° 65° 44° 122° 60° 93° 90° 110° 30° 66°

VERTICALLY OPPOSITE ANGLES ARE EQUAL 25/02/2019 VERTICALLY OPPOSITE ANGLES ARE EQUAL

25/02/2019 When two lines intersect, two pairs of vertically opposite angles are formed. a d b c a = c and b = d Vertically opposite angles are equal

25/02/2019 b 35 a Find the size of the angles a and b giving a reason

ANGLES AT A POINT ADD UP TO 360° 25/02/2019 ANGLES AT A POINT ADD UP TO 360°

Angles around a point add up to 360 25/02/2019 Angles around a point add up to 360 b a c d a + b + c + d = 360 because there are 360 in a full turn.

25/02/2019 Example a 75o 85o 80o + Angle a = 360 - (85 + 75 + 80) 240 Angle a = 360 - (85 + 75 + 80) = 360 - 240 = 120o

25/02/2019 Examples You might also need to use other angle rules and knowledge to help you solve problems involving angles at a point 167° a 69° 68° d 103° 43° c 43° b 137°

ANGLES IN A TRIANGLE ADD UP TO 180° 25/02/2019 ANGLES IN A TRIANGLE ADD UP TO 180°

The angles in a triangle add up to 180° 25/02/2019 a b c For any triangle, a + b + c = 180° The angles in a triangle add up to 180°

25/02/2019 Examples 65o Calculate angle a a 27o Calculate angle a a

Calculate angles a, b and c 25/02/2019 Examples Calculate angles a, b and c a b c Since the triangle is equilateral, angles a, b and c are all 60o (180÷3)

25/02/2019 90° 60° 70° 26° 55° 90°

ANGLES IN A QUADRILATERAL ADD UP TO 360° 25/02/2019 ANGLES IN A QUADRILATERAL ADD UP TO 360°

The angles in a quadrilateral add up to 360° 25/02/2019 d c a b For any quadrilateral, a + b + c + d = 360° The angles in a quadrilateral add up to 360°

25/02/2019 Angles TASK 1 EXTENSION 1) Calculate the value of the missing angles below: j 150º 80º 30º EXTENSION 1) Calculate the value of x below:

25/02/2019 Solutions EXTENSION 1) Calculate the value of x below: j 100º 150º 80º 30º EXTENSION 1) Calculate the value of x below: 3x + 10 + 2x – 4 + x + 8 + 28 = 360 6x + 42 = 360 6x = 318 x = 53

Find the missing angles, giving reasons for your answers 25/02/2019 Find the missing angles, giving reasons for your answers 1) 2) 97° 75° 130° k i j 85° 90° 52°

25/02/2019 Solutions 2) 1) 97° 121° k 75° 130° 52° j 90° i 70° 85° 52° Vertically opposite angles are equal Angles in a quadrilateral add to 360° Angles in a quadrilateral add to 360°

BASE ANGLES IN AN ISOSCELES TRIANGLE ARE EQUAL 25/02/2019 BASE ANGLES IN AN ISOSCELES TRIANGLE ARE EQUAL

Base angles in an isosceles triangle are equal 25/02/2019 Base angles in an isosceles triangle are equal

Calculate angles x and y 25/02/2019 Example a 65o Calculate angle a b Angle a = 65o (base angles of an isosceles triangle are equal). Angle b = 180 –(65 + 65) = 180 – 130 = 50o Calculate angles x and y y 130o x

25/02/2019 650 1) 2) 3) 4) 500 600 500 x 500 800 x x 400 x 200 400 5) 6) 7) 300 8) 450 x 700 700 x x x 600 11) 10) 9) x 12) 600 400 200 350 72.50 x 800 400 300 x x

ALTERNATE ANGLES ARE EQUAL, AND CORRESPONDING ANGLES ARE EQUAL 25/02/2019 ALTERNATE ANGLES ARE EQUAL, AND CORRESPONDING ANGLES ARE EQUAL

25/02/2019 Corresponding angles are equal Alternate angles are equal Interior angles add up to 180° a a a b b b a = b a = b a + b = 180° Look for an F-shape Look for a Z-shape Look for a C- or U-shape

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25/02/2019 x 100o y z 60o

25/02/2019 105o z 55o x y

25/02/2019 58o a b e c g f d 70o h