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
