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Pls help all the sums below
no 1 ab
no2 a
Do give explanation and show workout

Pls help all the sums below no 1 ab no2 a Do give explanation and show workout-example-1

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Answer: Number 1 (a)

a = 22.5 Hence 2a = 45 and 3a = 67.5

Number 1 (b)

b = 244 and c = 26

Number 2 (a)

a = 70 and b = 20

Step-by-step explanation: From the figure in number in number 1(a), we have an isosceles triangle with sides AB and AC being equal in dimensions (as shown by the markings). Therefore angles B and C are also equal (angles subtended by equal sides in an isosceles triangle). If angle B is 3a then angle C equals 3a as well. if the sum of the interior angles of a triangle equals 180, then;

2a+3a+3a = 180

8a = 180

Divide both sides of the equation by 8

a = 22.5

From the figure shown in number 1(b), we have two isosceles triangles. The first on is ABC with sides AC and BC being of equal length and angles A and B being of equal measurement. The second one is triangle ABD with sides AD and BD being of equal length and angles A and B being of equal measurement. In triangle ABC,

A+B+ 64 = 180 (Sum of the interior angles of a triangle)

A+B = 180 - 64

A+B = 116

Remembering that A and B are of equal measurement, we divide 116 by 2 to arrive at angles A and B

Therefore, angle A = 58, and angle B = 58

If angle B equals 58, then in triangle ABD, c is calculated as 58 - 32

Therefore C equals 26.

To calculate angle D (in triangle ABD)

Angle D = 180 - (32+32)

Angle D = 180 - 64

Angle D = 116

Therefore to calculate b;

Remember that the addition of angle D and angle b equals 360 (Sum of angles on a point) Hence we have

D + b = 360

116 + b = 360

Subtract 116 from both sides of the equation

b = 244

From the figure given in number 2(a), we also have two triangles. The first one is isosceles triangle ABD with sides AB and BD being equilateral. Therefore angle A and angle D are equal.

A+B+D = 180 (Sum of the interior angles in a triangle)

A+D+40 = 180

Subtract 40 from both sides of the equation

A+D = 140

Remembering that A and D are equal, divide 140 in two

Angle A = 70, and angle D = 70.

Therefore a = 70

To calculate b, we move on to the second isosceles triangle, triangle BCD with sides BC and BD being equal. That makes angle C and D equal (angles subtended by equal sides of an isosceles triangle)

Angle B measures 140. This is because the line from point D that divides point B gave rise to angle 40 and the other one is 180-40 which equals 140 (Sum of angles on a straight line). If angle B measures 140, and angles C and D are equal, then

C + D = 180 - 140

C + D = 40. We further divide the answer into two

We arrive at C = 20 and D = 20

Therefore b = 20.

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