How do I find the measures of the numbered angles in each kite below?

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1 Answer
Somebody N.
Dec 5, 2017

See below.

Explanation:

enter image source here

Figure 1.

#/_ABC = /_ADC#

#AC and BD# are perpendicular.

#AC# bisects #/_BCD and /_BAD#

Looking at triangle #ABC#

#/_BAC=44/2=22^@#

#/_BCA=120/2=60^@#

#:.#

Sum of angles in a triangle equal #180^@#

#/_ABC=180^@-(60^@+22^@)=98^@#

#/_ABC = /_ADC# so 1 and 2 are #color(blue)(98^@)#

Figure 2:

#BD and AC# are perpendicular:

So 1 is #color(blue)(90^@)#

Looking at triangle #ADE#

Sum of angles in a triangle equal #180^@#

#:.#

#/_ADE=180^@-(90^@+70^@)=20^@#

2 is #color(blue)(20^@)#

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