Answer:
measure of angle ADC = 100°
measure of angle DCB = 39°
Step-by-step explanation:
We know that all the interior angles of a triangle add up to equal 180°, so we can set up an equation based on what we know from the figure (Angle C is the sum of [tex](4x-1)[/tex]° and [tex](2x+17)[/tex]°):
180° = 43° + 61° + [[tex](4x-1)[/tex]° + [tex](2x+17)[/tex]°]
180° = 43° + 61° + [tex]6x +16[/tex]°
180° = 104° + 16° + [tex]6x[/tex]
180° = 120° + [tex]6x[/tex]
60° = [tex]6x[/tex]
10° = [tex]x[/tex]
Now that we know the value of [tex]x[/tex], we can easily plug in 10° for [tex]x[/tex] in the angles we need to find.
The second angle we need to find uses [tex]x[/tex], so we can now find it. Angle DCB is, according to the figure, equal to [tex]4x-1[/tex].
[tex]4x-1[/tex]
[tex]4(10)-1\\40-1\\39[/tex]
Thus, the measure of angle DCB is equal to 39°.
However, angle ADC is defined in terms of [tex]y[/tex], so we'll have to find the value of [tex]y[/tex]. This is easy, however, because the two angles using [tex]y[/tex] meet together to form a straight line. Since we know that a straight line has an angle measure of 180°, we can once again set our equation equal to 180°.
180° = [tex](3y+7)+(3y-13)[/tex]
180° = [tex]6y[/tex] + 7° - 13°
180° = [tex]6y[/tex] - 6°
186° = [tex]6y[/tex]
31° = [tex]y[/tex]
Now, we'll simply substitute 31° for [tex]y[/tex] in the measure of angle ADC:
[tex]3y+7\\3(31)+7\\93+7\\100[/tex]
Therefore, the measure of angle ADC is equal to 100°.
