Let's analyze and solve the question:

Problem Analysis

Given:

1. Angles $\angle ADC$ and $\angle CBD$ are complementary, meaning their measures add up to $90^\circ$.
2. $\angle ADC$ is twice the size of $\angle CBD$.

Step-by-Step Solution

Let:

• $x$ be the measure of $\angle ADC$.
• $y$ be the measure of $\angle CBD$.

According to the conditions:

1. $x + y = 90$ (since they are complementary).
2. $x = 2y$ (since $\angle ADC$ is twice $\angle CBD$).

Substitute $x = 2y$ into $x + y = 90$:

$2y + y = 90$ $3y = 90$ $y = 30$

Now, substitute $y = 30$ back to find $x$: $x = 2 \times 30 = 60$

Answer for Part 3b

The measure of $\angle ADC$ is $60^\circ$, so the correct answer is:

• C. $60^\circ$

Would you like more details or have any questions?

Related Questions:

1. What would the measure of $\angle CBD$ be if $\angle ADC$ was three times $\angle CBD$?
2. How would you solve for the angles if $\angle ADC$ and $\angle CBD$ were supplementary instead of complementary?
3. If $\angle ADC$ was half of $\angle CBD$, what would their measures be?
4. Can you verify the complementary nature of two angles if only one angle measure is given?
5. How does knowing one angle in a complementary pair help find the other angle?

Tip:

Remember, complementary angles always add up to $90^\circ$, and supplementary angles add up to $180^\circ$.