Question

practice
example 1
find the measure of each angle.

1. find ( mangle abc ) if ( mangle abd = 70^circ ) and ( mangle dbc = 43^circ ).
2. if ( mangle ebc = 55^circ ) and ( mangle ebd = 20^circ ), find ( mangle 2 ).
3. find ( mangle abd ) if ( mangle abc = 110^circ ) and ( mangle 2 = 36^circ ).

practice • spiral review • extra practice

Explanation:

Problem 1

Step1: Identify angle addition

$\angle ABC = \angle ABD + \angle DBC$

Step2: Substitute values

$m\angle ABC = 70^\circ + 43^\circ$

Step3: Calculate sum

$m\angle ABC = 113^\circ$

Step1: Analyze angle relationships

$\angle EBC = \angle EBD + \angle 2$

Step2: Rearrange to solve for $\angle 2$

$m\angle 2 = m\angle EBC - m\angle EBD$

Step3: Substitute values

$m\angle 2 = 55^\circ - 20^\circ$

Step4: Calculate difference

$m\angle 2 = 35^\circ$

Step1: Identify angle addition

$\angle ABC = \angle ABD + \angle 2$

Step2: Rearrange to solve for $\angle ABD$

$m\angle ABD = m\angle ABC - m\angle 2$

Step3: Substitute values

$m\angle ABD = 110^\circ - 36^\circ$

Step4: Calculate difference

$m\angle ABD = 74^\circ$

Answer:

$113^\circ$

Problem 2