Question

please solve for the missing angles. 18. 19. 33° 4 1 3 59° 2 m∠1 = 83° m∠2 = __ m∠3 = m∠4 = __

Explanation:

Step1: Use angle - sum property of a straight - line

The sum of angles on a straight - line is 180°. For the straight - line with angles 33°, 59° and ∠1, we have 33°+59°+m∠1 = 180°.
$m\angle1=180^{\circ}-(33^{\circ} + 59^{\circ})=88^{\circ}$

Step2: Use vertical - angle property

Vertical angles are equal. ∠1 and ∠3 are vertical angles, so m∠3=m∠1 = 88°.

Step3: Use vertical - angle property again

∠2 and the angle composed of 33° and 59° are vertical angles. The angle composed of 33° and 59° is 33°+59° = 92°. So m∠2 = 92°.

Step4: Use vertical - angle property for ∠4

∠4 and ∠2 are vertical angles, so m∠4=m∠2 = 92°.

Answer:

$m\angle1 = 88^{\circ}$
$m\angle2 = 92^{\circ}$
$m\angle3 = 88^{\circ}$
$m\angle4 = 92^{\circ}$