Question

ASE

BCDE is a trapezium with angle CDE = 90°. ABEF is a straight line.
Q2)
D
Diagram
accurately
1159
А
11030
E
F
B
Work out the size of the angle marked x.

Answer 1

so we will get a lot of teiangles here.

90°+x+CED=180°

also CED+DEF=180°(half circle, 360/2)

CED+103°=180°

CED=180-103=77°

77°+90°+X/2=180°

x/2=180-167=13°

Answer 2

128 deg

Explanation:

The sum of the measures of the angles of a polygon of n sides is

(n - 2)180

A trapezium has 4 sides, so the sum of the measures of the angles is

(4 - 2)180 = 2(180) = 360

m<CBE + m<C + m<D + m<DEB = 360

Angles ABC and CBE are a linear pair so the sum of their measures is 180 deg.

m<ABC + m<CBE = 180

115 + m<CBE = 180

m<CBE = 65

m<C = x

m<D = 90

Angles DEB and DEF are a linear pair so the sum of their measures is 180 deg.

m<DEB + m<DEF = 180

m<DEB + m<103 = 180

m<DEB = 77

m<CBE + m<C + m<D + m<DEB = 360

65 + x + 90 + 77 = 360

x + 232 = 360

x = 128

Answer: 128 deg