Answer:
22. 90°
23. 16°
24. 74°
25. 74°
26. 148°
27. 32°
Step-by-step explanation:
22. The measure of the angle BCD is 90 degrees as it is a right angle.
23. The measure of the angle ABD is equal to the measure of BDC, and it is 16 degrees.
24. The angle CBE is equivalent to the angle CBD.
We know that BCD form a right triangle. The three angles must add 180 degrees, so we have:
[tex]m\angle BDC+m\angle DCB+m\angle CBD=180^{\circ}\\\\16^{\circ}+90^{\circ}+m\angle CBD=180^{\circ}\\\\+m\angle CBD=180^{\circ}-90^{\circ}-16^{\circ}=74^{\circ}[/tex]
25. The measure of the angle ADE is equivalent to CBE, so it is 74 degrees.
26. The measure of the angle AEB can be calculated from the isosceles triangle formed by AEB, from which we know 2 of the 3 angles. They have the same measure (16 degrees), so if we substract from 180 degrees (the sum of the 3 triangle angles) the 2 angles of 16 degrees we have:
[tex]m\angle AEB=180^{\circ}-2*16^{\circ}=180^{\circ}-32^{\circ}=148^{\circ}[/tex]
27. The measure of the angle DEA can be calculated substracting from the flat angle DEB (180 degrees) the measure of the angle AEB:
[tex]m\angle DEA=180^{\circ}-m\angle AEB=180^{\circ}-148^{\circ}=32^{\circ}[/tex]
