Question

question 9 of 10 what is the measure of ∠ace shown in the diagram below? a. 65° b. 35° c. 70° d. 130°

Explanation:

Step1: Recall angle - secant rule

The measure of an angle formed by two secants is half the positive difference of the measures of the intercepted arcs. Let the larger arc be $\overset{\frown}{AE}=100^{\circ}$ and the smaller arc be $\overset{\frown}{BD} = 30^{\circ}$.

Step2: Apply the formula

The measure of $\angle ACE=\frac{1}{2}(\text{measure of }\overset{\frown}{AE}-\text{measure of }\overset{\frown}{BD})$.
So, $\angle ACE=\frac{1}{2}(100 - 30)$.

Step3: Calculate the result

$\frac{1}{2}(100 - 30)=\frac{1}{2}\times70 = 35^{\circ}$.

Answer:

B. 35°