Given:
Two angles form a linear pair.
The measure of one angle is z and the measure of the other angle is 2.4 times z plus 10°.
To find:
The measure of the smallest and biggest angle.
Solution:
Two angles form a linear pair. The measure of one angle is z.
The measure of the other angle is 2.4 times z plus 10°, i.e., [tex]2.4z+10^\circ[/tex].
We know that if two angles form a linear pair then their sum is 180 degrees.
[tex]z+(2.4z+10^\circ)=180^\circ[/tex]
[tex]3.4z=180^\circ -10^\circ[/tex]
[tex]3.4z=170^\circ[/tex]
Divide both sides by 3.4.
[tex]z=\dfrac{170^\circ}{3.4}[/tex]
[tex]z=50^\circ[/tex]
Now, the measure of other angle is:
[tex]2.4z+10^\circ =2.4(50^\circ)+10^\circ[/tex]
[tex]2.4z+10^\circ =120^\circ+10^\circ[/tex]
[tex]2.4z+10^\circ =130^\circ[/tex]
Therefore, the measure of the smaller angle is [tex]50^\circ[/tex] and the measure of the bigger angle is [tex]130^\circ[/tex].
