IDNLearn.com: Your reliable source for finding expert answers. Get thorough and trustworthy answers to your queries from our extensive network of knowledgeable professionals.
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].
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Discover the answers you need at IDNLearn.com. Thank you for visiting, and we hope to see you again for more solutions.