Given that angle 2 has measure $m\angle 2=a+15°$ and angle 3 has measure $m\angle 3=a+35°$, find the value of $a$ such that $m\angle 2=m\angle 3$.

• A. $a=20$
• B. $a=-10$
• C. $a=10$
• D. $a=50$

Answer: (B)

Verified step by step guidance

1. Identify the given angle measures: \(m\angle 2 = a + 15^\circ\) and \(m\angle 3 = a + 35^\circ\).
2. Set the two angle measures equal to each other since the problem states \(m\angle 2 = m\angle 3\).
3. Write the equation: \(a + 15 = a + 35\).
4. Subtract \(a\) from both sides to simplify the equation: \$15 = 35$.
5. Recognize that this simplification leads to a contradiction, so re-check the problem conditions or consider if there is additional context (such as angles being equal under certain conditions) to solve for \(a\).