Answer:
See below.
Explanation:
9.
Property of a rhombus:
In a rhombus, the diagonals are perpendicular.
The sum of the measures of the angles of a triangle is 180 deg.
Since the diagonals are perpendicular, the angles formed by the intersection of the diagonals are right angles and measure 90 deg.
m<ABD + m<CAB + 90 = 180
50 + m<CAB + 90 = 180
m<CAB + 140 = 180
(i) m<CAB = 40
The diagonals of a rhombus divide the rhombus into 4 congruent triangles.
Call the point of intersection of the diagonals E.
Triangles CEB and AEB are congruent.
m<BCA = m<DCA = 40
m<BCD = m<BCA + m<DCA = 40 + 40
(ii) m<BCD = 80
m<CDB = m<ADB = 50
m<ADC = m<CDB + m<ADB = 50 + 50
(iii) m<ADC = 100
10.
There are two angles labeled z. One is near point E and one is near point O. One of them probably is x.
Two angles measure 60 and 80. Add them to get 140.
z (near point O) and the 140 deg angle are a linear pair. their measures add to 180 deg.
z + 140 = 180
z = 40 (This is the z near point O.)
z (near point O) and 60 deg add to an interior angle of the parallelogram.
z + 60 = 40 + 60 = 100
The interior angle at vertex O measures 100 deg.
Adjacent interior angles of a parallelogram are supplementary.
100 + y = 180
y = 80
The two angles labeled z are alternate interior angles. Since the sides of a parallelogram are parallel, the two angles labeled z are congruent and measure 40 deg.
z = 40 (This is angle z near point E)