How to Find Unknown Angles

How to Find Unknown Angles example 1 84 x Find the m x 1st: think of what you know or what the problem tells you -the two angles are a linear pair (form a straight line together), so they must add to = 180°. 2nd: write an equation based on what you know x + 84 = 180 3rd: solve the equation -84 = -84 x = 96 4th: answer the question the missing angle is  x = 96 Missing angle is 96°

How to Find Unknown Angles example 2 J Find the measure of each unknown angle O 4x° x° K M 1st: think of what you know or what the problem tells you -since the index (box in the corner of the angle) tells us that <JKM is right, it must = 90°. -the 4x angle and the x angles must be complementary and add together to 90° 2nd: write an equation based on what you know 4x + x = 90 3rd: solve the equation 5x = 90 x = 18 4th: answer the question the missing angles were x and 4x, so plug 18 back in as x and simplify them both x=18, and 4(18)=72 Missing angles are 18° and 72°

How to Find Unknown Angles example 3 D F E H 3x x Find the measure of each unknown angle 1st: think of what you know or what the problem tells you -the two angles are a linear pair (form a straight line together), so they must add to = 180°. 2nd: write an equation based on what you know x + 3x = 180 3rd: solve the equation 4x = 180 x = 45 4th: answer the question the missing angles were x and 3x, so plug 45 back in as x and simplify them both x=45, and 3(45)=135 Missing angles are 45° and 135°

How to Find Unknown Angles example 4 m 4 = 2x +5 m 5 = x + 30 Find the m 4 and m 6 4 5 6 1st: think of what you know or what the problem tells you -  4 and 5 are vertical angles, so they are congruent (= measure) -  4 and 6 are supp. / form a linear pair (form a straight line), so they must add to = 180°. 2nd: write an equation based on what you know  4 =  5 so 2x + 5 = x + 30 3rd: solve the equation x + 5 = 30 x = 25 4th: answer the question plug 25 back in as x to find missing angles  4 = 2x + 5  4 = 2(25) + 5  4 = 55 and also  4 +  6 = 180, so  6 = 125 Missing angles are  4=55° and  6=125°

How to Find Unknown Angles example 5 Try one if you are only given a description! Angle a and angle b are supplementary angles. If angle a is one-fifth the measure of b, what is the measure of each angle? Draw your own diagram! 1st: think of what you know Since <a and <b are supplementary, they must add to 180°. If <a is unknown, call it x. If <a is one-fifth of <b, then <b must be 5x because it will be 5 times bigger. 2nd: write an equation x + 5x = 180 3rd: solve the equation 6x = 180 6 6 x = 30 4th: answer the question <a = 30° and <b = 150° a b x 5x