1 Answer

Loginx · Answer 1 · 2022-05-08T22:10:43+0000

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.,
$2.4z+10^\circ$ .

We know that if two angles form a linear pair then their sum is 180 degrees.

$z+(2.4z+10^\circ)=180^\circ$

$3.4z=180^\circ -10^\circ$

$3.4z=170^\circ$

Divide both sides by 3.4.

$z=(170^\circ)/(3.4)$

$z=50^\circ$

Now, the measure of other angle is:

$2.4z+10^\circ =2.4(50^\circ)+10^\circ$

$2.4z+10^\circ =120^\circ+10^\circ$

$2.4z+10^\circ =130^\circ$

Therefore, the measure of the smaller angle is
$50^\circ$ and the measure of the bigger angle is
$130^\circ$ .

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