Answer:
Option (2). x = 20°
Step-by-step explanation:
In the figure attached,
ΔABC is an equilateral triangle.
By the property of equilateral triangle, all sides of the triangle are equal and measure of all angles of the triangle is 60°.
By this property,
m∠B = 60°
and y = 46 - 16 = 30
By applying Sine rule in ΔBCD,
[tex]\frac{\text{sin}60}{BD}=\frac{\text{sin}80}{46}=\frac{\text{sin}(\angle CBD)}{DC}[/tex]
[tex]\frac{\text{sin}80}{46}=\frac{\text{sin}(\angle CBD)}{y}[/tex]
sin(∠CBD) = [tex]\frac{30\times \text{sin}80}{46}[/tex]
= 0.6423
m∠CBD = 39.96
≈ 40°
m∠ABD = 60° - 40°
= 20°
Therefore, Option (2). 20° will be the answer.
