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Two angles of a quadrilateral measure 160° and 20°. The other two angles are in a ratio of 7:11. What are the measures of those two angles?

the sum of all the angles is 360º

160 + 20 + 7 k + 11 k = 360 ... 18 k = 180

looks like 70º and 110º

Did you know?

Did you know that in any quadrilateral, the sum of all four angles is always 360 degrees? Knowing this, we can determine the measures of the other two angles in the given quadrilateral. Since two angles are already given as 160° and 20°, we can subtract their sum from 360 to find the remaining angle measure. In this case, the sum of the two given angles is 160° + 20° = 180°. Subtracting this from 360, we have 360° - 180° = 180°. Now, we know that the other two angles in the quadrilateral must sum up to 180°. Given that these two angles are in a ratio of 7:11, we can set up an equation to solve for their measures. Let's represent these angles as 7x° and 11x°. According to the ratio, the sum of these two angles is 7x° + 11x° = 18x°. Since the sum of the other two angles is 180°, we have the equation 18x° = 180°. Solving for x, we divide both sides of the equation by 18, giving us x = 10°. Finally, plugging x back into the ratio, we get the measures for the other two angles as 7x° = 7 * 10° = 70°, and 11x° = 11 * 10° = 110°. Therefore, the measures of the other two angles in the given quadrilateral are 70° and 110°.