Question

In the figure, \( \triangle ODC \sim \triangle OBA \). If \( \angle BOC = 125^\circ \) and \( \angle CDO = 70^\circ \), then the value of \( \angle OAB \) will be: 

• A. 55°
• B. 60°
• C. 65°
• D. 70°

Hint:

In similar triangles, corresponding angles are equal and corresponding sides are proportional. Use angle-sum property to find missing angles.

Answer 1

The Correct Option is A

Step 1: Given information.
In \( \triangle ODC \) and \( \triangle OBA \), we are told that \( \triangle ODC \sim \triangle OBA \). Given that: \[ \angle BOC = 125^\circ, \quad \angle CDO = 70^\circ \]
Step 2: Find \( \angle DOC \).
Since \( \angle BOC = 125^\circ \) (vertically opposite angle), \[ \angle DOC = 180^\circ - 125^\circ = 55^\circ \]
Step 3: Relation from similarity.
From similarity \( \triangle ODC \sim \triangle OBA \), corresponding angles are equal: \[ \angle CDO = \angle OAB \] But \( \angle CDO = 70^\circ \). However, we must check consistency with the interior sum. In \( \triangle ODC \): \[ \angle ODC + \angle DOC + \angle OCD = 180^\circ \] \[ 70^\circ + 55^\circ + \angle OCD = 180^\circ \] \[ \angle OCD = 55^\circ \]
Step 4: Corresponding angles in similar triangles.
Hence, \( \angle OAB = \angle OCD = 55^\circ \). Step 5: Final answer.
\[ \boxed{\angle OAB = 55^\circ} \]