ab is tangent to ⊙c at point b and ad is tangent to ⊙c at point d. what is m∠a? 34° 62° 56° 124°
ab is tangent to ⊙c at point b and ad is tangent to ⊙c at point d. what is m∠a? 34° 62° 56° 124°
Answer
Explanation:
Step1: Recall tangent - radius property
A tangent to a circle is perpendicular to the radius at the point of tangency. So, $\angle ABC = 90^{\circ}$ and $\angle ADC=90^{\circ}$.
Step2: Use the sum of angles in a quadrilateral
The sum of the interior angles of a quadrilateral $ABCD$ is $360^{\circ}$. In quadrilateral $ABCD$, we know that $\angle ABC = 90^{\circ}$, $\angle ADC = 90^{\circ}$ and $\angle BCD=124^{\circ}$. Let $\angle BAD = x$. Then, by the angle - sum property of a quadrilateral: $x + 90^{\circ}+90^{\circ}+124^{\circ}=360^{\circ}$.
Step3: Solve for $\angle A$
Simplify the equation: [ \begin{align*} x+304^{\circ}&=360^{\circ}\ x&=360^{\circ}- 304^{\circ}\ x&=56^{\circ} \end{align*} ]
Answer:
$56^{\circ}$