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one side of a triangle is produced , the exterior angle so formed is 140° . if the corresponding interior opposite angles are in the ratio 3:4, find the measure of all the angles of the triangle |
| Answer» ION ✪One side of a triangle is produced, the exterior angle so formed is 140°. If the corresponding interior OPPOSITE angles are in the ratio 3:4, find the measure of all the angles of the triangle.✪ Given ✪Exterior angle = 140°Ratio of opposite angles = 3:4✪ To find ✪The measure of all angles.✪ Solution ✪Let the opposite angles are 3x° and 4x°.Since the sum of opposite TWO angles is equal to the exterior angle, we can say-⇒ ⇒ ⇒ ✪ Hence ✪x = 203x° = (3×20)° = 60°4x° = (4×20)° = 80°Let the 3RD angle be y°.As we KNOW that the sum of all angles of a triangle is 180°, we can say-⇒ ⇒ ⇒ So, 3rd angle = y° = 40°✪ Therefore ✪All the angles of the triangle are 60°, 80° and 40°. ๑ Hope this helps you. ๑ | |