Question

Please help with these two questions​

Answer 1

Answer:

10. Let m<Y = y.

Then,

m<Y + m<X +m<Z = 180 [ Sum of angles of triangle is 180 degrees]

or, y + (6x-23) + (4x + 9) = 180

or, y + 10x -14 = 180

or, y = 194 - 10x

or, m<Y = 194 - 10x

12. Solution,

a.  m<1 = 60 degrees [Each angles of equilateral triangle is equal to 60 degrees]

b.  In triangle WYZ,

m<Z + m<ZWY + m<ZYW =180 [Sum of angles of triangle is 180]

or, 138 + m<ZWY +m<ZWY =180 [Base angles of isosceles triangle are equal, i.e. m<ZYW = m <ZWY]

or, 2 (m<ZWY) = 180 -138 = 42

or, m<ZWY = 21 = m<ZYW

or, m<3 = 21 = m<5

c. Solution,

m<XWY = m<2 + m<3 [Addition axiom]

or, 60 = m<2 + 21 [Each angle of equilateral triangle is 60]

or, m<2 = 39

d. Solution,

m<4 + m<5 =60 [<XYW = 60 ]

or, m<4 + 21 = 60

or, m<4 = 39