Question

If \( \triangle ODC \sim \triangle OBA \) and \( \angle BOC = 125^\circ \), then \( \angle DOC = ? \)

 

• A. \( 60^\circ \)
• B. \( 55^\circ \)
• C. \( 50^\circ \)
• D. \( 65^\circ \)

Hint:

Remember the properties of similar triangles (corresponding angles are equal), vertically opposite angles (they are equal), and angles on a straight line (their sum is \( 180^\circ \)).

Answer 1

The Correct Option is B

Step 1: Understand the properties of similar triangles.
If \( \triangle ODC \sim \triangle OBA \), then their corresponding angles are equal. This implies: \[ \angle DOC = \angle BOA \] \[ \angle ODC = \angle OBA \] \[ \angle OCD = \angle OAB \] Step 2: Use the property of vertically opposite angles.
From the given diagram, \( \angle BOC \) and \( \angle AOD \) are vertically opposite angles. Therefore, \[ \angle AOD = \angle BOC = 125^\circ \] Step 3: Angles on a straight line.
The angles \( \angle BOC \) and \( \angle DOC \) are adjacent angles on a straight line (assuming \( D, O, B \) are collinear or \( C, O, A \) are collinear, which seems to be the case from the diagram). Therefore, their sum is \( 180^\circ \): \[ \angle BOC + \angle DOC = 180^\circ \] Step 4: Solve for \( \angle DOC \).
We are given \( \angle BOC = 125^\circ \). Substituting this value into the equation from Step 3: \[ 125^\circ + \angle DOC = 180^\circ \] \[ \angle DOC = 180^\circ - 125^\circ \] \[ \angle DOC = 55^\circ \]