Find the value of the lettered angles in each of the following ( see image ). Please show workings.

The only given angles are 60° , 10° , 40°​

Step-by-step explanation:

s + 40 + 60 = 180 {angle sum property}

s + 100        = 180

               s = 180 - 100

               s = 80

This figure is a cyclic quadrilateral. sum of opposite angles are 180

s + v + 60 + 10 = 180

80 + v + 60 + 10 = 180

             v + 150  = 180

                       v = 180 - 150

                      v = 30

y+ 10 + v  = 180 {angle sum property}

    y + 10 + 30 = 180

             y + 40 = 180

                   y = 180 - 40

                  y = 140

9514 1404 393

  r = 80°, s = 80°, t = 10°, u = 60°, v = 30°

Step-by-step explanation:

Working clockwise from the left side, we can name the points on the circle as A, B, C, D. The given inscribed angles are half the measure of the arcs they intercept, so we have ...

  arc BD = 2×40° = 80°

  arc DA = 2×60° = 120°

  arc CD = 2×10° = 20°

From these measures, we can deduce the measures of the individual arcs as ...

  arc AB = 360° -BD -DA = 360° -80° -120° = 160°

  arc BC = BD -CD = 80° -20° = 60°

Then the angle measures of interest are ...

  r = AB/2 = 80°

  s = AB/2 = 80°

  t = CD/2 = 10°

  u = DA/2 = 60°

  v = BC/2 = 30°

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

how is that middle school

step-by-step explanation: