IDNLearn.com: Your one-stop destination for reliable answers to diverse questions. Explore a wide array of topics and find reliable answers from our experienced community members.
Sagot :
To solve for [tex]\( m \angle CBD \)[/tex] given the information [tex]\( m \angle ABC = 90^\circ \)[/tex] and [tex]\( m \angle ABD = 25^\circ \)[/tex], follow these steps:
1. Given: [tex]\( m \angle ABC = 90^\circ \)[/tex] and [tex]\( m \angle ABD = 25^\circ \)[/tex].
2. Angle Addition Postulate: This postulate states that if a point D lies in the interior of [tex]\( \angle ABC \)[/tex], then
[tex]\[ m \angle ABD + m \angle CBD = m \angle ABC \][/tex]
Applying this postulate, we have:
[tex]\[ m \angle ABD + m \angle CBD = m \angle ABC \][/tex]
3. Substitution Property of Equality: Substitute the given values into the equation:
[tex]\[ 25^\circ + m \angle CBD = 90^\circ \][/tex]
4. Solving for [tex]\( m \angle CBD \)[/tex]: To find [tex]\( m \angle CBD \)[/tex], isolate [tex]\( m \angle CBD \)[/tex] on one side of the equation:
[tex]\[ m \angle CBD = 90^\circ - 25^\circ \][/tex]
5. Conclusion:
[tex]\[ m \angle CBD = 65^\circ \][/tex]
Thus, the measure of [tex]\( \angle CBD \)[/tex] is [tex]\( 65^\circ \)[/tex].
1. Given: [tex]\( m \angle ABC = 90^\circ \)[/tex] and [tex]\( m \angle ABD = 25^\circ \)[/tex].
2. Angle Addition Postulate: This postulate states that if a point D lies in the interior of [tex]\( \angle ABC \)[/tex], then
[tex]\[ m \angle ABD + m \angle CBD = m \angle ABC \][/tex]
Applying this postulate, we have:
[tex]\[ m \angle ABD + m \angle CBD = m \angle ABC \][/tex]
3. Substitution Property of Equality: Substitute the given values into the equation:
[tex]\[ 25^\circ + m \angle CBD = 90^\circ \][/tex]
4. Solving for [tex]\( m \angle CBD \)[/tex]: To find [tex]\( m \angle CBD \)[/tex], isolate [tex]\( m \angle CBD \)[/tex] on one side of the equation:
[tex]\[ m \angle CBD = 90^\circ - 25^\circ \][/tex]
5. Conclusion:
[tex]\[ m \angle CBD = 65^\circ \][/tex]
Thus, the measure of [tex]\( \angle CBD \)[/tex] is [tex]\( 65^\circ \)[/tex].
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.