Question

finding the unknown angles
for the diagram shown, find the measures of angles 4, 5, and 6.
m∠4 = degrees
m∠5 = degrees
m∠6 = degrees

Explanation:

Step1: Use vertical - angle property

$m\angle4 = 57^{\circ}$ (vertical angles are equal)

Step2: Use linear - pair property

$m\angle5=180 - 57=123^{\circ}$ (linear pair sums to 180°)

Step3: Use angle - sum property of triangle

$m\angle6 = 180-(35 + 123)=22^{\circ}$ (sum of angles in a triangle is 180°)

Answer:

$m\angle4 = 57$ degrees
$m\angle5 = 123$ degrees
$m\angle6 = 22$ degrees