Calculate the size of each lettered angle
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angle DAB = angle BDA ( angle opposite to equal sides are equal)
In ∆ABD,
angle DAB + angle BDA + angle ABD = 180° ( sum of all interior angles of a triangle is 180°)
70° + angle ABD = 180°
angle ABD = 110°
angle ABD + y = 180° ( linear pair axiom)
110° + y = 180°
y = 70°
angle DBC = angle BCD ( angle opposite to equal sides are equal)
In ∆DBC,
angle y + y + angle BDC = 180° ( sum of all interior angles of a triangle is 180°)
140° + angle BDC = 180°
angle BDC = 40°
angle BDA + angle BDC + x = 180° ( linear pair axiom)
35° + 40° + x = 180°
x = 180° - (35°+40°)
x = 105°
In ∆ABD,
angle DAB + angle BDA + angle ABD = 180° ( sum of all interior angles of a triangle is 180°)
70° + angle ABD = 180°
angle ABD = 110°
angle ABD + y = 180° ( linear pair axiom)
110° + y = 180°
y = 70°
angle DBC = angle BCD ( angle opposite to equal sides are equal)
In ∆DBC,
angle y + y + angle BDC = 180° ( sum of all interior angles of a triangle is 180°)
140° + angle BDC = 180°
angle BDC = 40°
angle BDA + angle BDC + x = 180° ( linear pair axiom)
35° + 40° + x = 180°
x = 180° - (35°+40°)
x = 105°
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