Calculating Angles.

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Presentation transcript:

Calculating Angles

6MG2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle. Objective: Understand how to find the degree measure of an angle based on other angles. Learning target: Answer at least 3 of the 4 angle questions correctly on the exit ticket.

How do we calculate the missing angle in a complementary pair? What is x? Set up an equation with the two angles adding to equal 90° x + 29° = 90° - 29° -29° x = 61°

What is y? y + 52° = 90° - 52° -52° y = 38°

How do we calculate the missing angle in a supplementary pair? What is m? Set up an equation with the two angles adding to equal 180° m + 108° = 180° - 108° -108° m = 72°

What is v? What is w? v + 120° = 180° - 120° -120° v = 60° w + 120° = 180° w = 60° This is not a coincidence! Either v or w could be used to complete a supplementary angle pair with the 120°, so they must be equal

What are vertical angles? Two non-adjacent angles formed when two lines cross. Vertical angles have the same degree measure. ∠v and ∠w are vertical angles

Which are vertical angles? Only ∠1 and ∠4 form a vertical angle pair because they are the only ones formed by 2 straight, intersecting lines.

What is t? The t and 110° are vertical angles, so t is also 110°

What are x, y, and z? The 44° and x are complementary angles, so x + 44° = 90° - 44° = -44° x = 46° x and z are vertical, so z = 46° x and y are supplementary, so 46 + y° = 180° - 46° = -46° y = 134°

Direct Station We will use whiteboards to work on problems combining all of the angle topics we have worked on so far: complementary, supplementary, vertical, and in triangles.

Collaborative Station You and your partner will write mathematical sentences using this sentence frame: An angle of ___ is ___________ with an angle of ___ because they __________________. You will have lists of possible numbers/words to fill in the blanks. Example: An angle of 35° is complementary with an angle of 45° because they add up to 90°. Write down the full sentence.

Independent Station You will continue ST Math’s unit on volume.