Question

4

A, B & C lie on a straight line.
D, C & E lie on a different straight line.
Angle
y
= 101° and angle
z
= 52°.
Work out
x
, explaining each stage of your working in the comment box.

Answer 1

x = 131°

Explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

y is an exterior angle of the triangle, then

∠ DCB + z = y , that is

∠ DCB + 52 = 101 ( subtract 52 from both sides )

∠ DCB = 49°

∠ DCB and x are adjacent angles and sum to 180°

∠ DCB + x = 180

49° + x = 180° ( subtract 49° from both sides )

x = 131°

Answer 2

X=131°

Explanation:

y= 101°

z= 52°

X= ?

BCD is a ∆

therefore y= Z + BCD angle (exterior angle of a ∆ is equal to the sum of opposite interior Angles)

angle BCD= y-z

= 101°-52°

=49°

also X= 180°- angle BCD (sum of angles on a straight line)

X= 180°-49°

X= 131°