If an exterior angle of a triangle measure 100° and its interior opposite angles are in the ratio 1:3.What is the meaure of its interior opposite angles?
Question
If an exterior angle of a triangle measure 100° and its interior opposite angles are in the ratio 1:3.What is the meaure of its interior opposite angles?
Solution
Sure, let's solve this step by step:
Step 1: We know that the sum of an interior angle and its corresponding exterior angle in a triangle is 180°. So, if the exterior angle is 100°, the angle inside the triangle that is adjacent to it is 180° - 100° = 80°.
Step 2: The problem states that the two interior opposite angles are in the ratio 1:3. This means that these two angles are parts of the 80° angle we just found.
Step 3: To find the measures of these two angles, we divide 80° by the total parts in the ratio, which is 1 + 3 = 4 parts.
Step 4: Each part is therefore 80° / 4 = 20°.
Step 5: The two interior opposite angles are then 120° = 20° and 320° = 60°.
So, the measures of the two interior opposite angles are 20° and 60°.
Similar Questions
The interior opposite angles of a triangle are in the ratio 1: 3. Given that, anexterior angle of the triangle is 80°. Find the value of interior opposite angles.a) 40°, 120° b) 30°,60° c) 20°,60° d) 90°, 60°
An exterior angle of a triangle is 108° and its interior opposite angles are in the ratio 4 : 5. The angles of thetriangle are
The measure of one of the interior angles of an isosceles triangle is 76°. What could be the measure, in degrees, of one of the other interior angles of the triangle?
he ratio between the interior angle and the exterior angle of a regular polygon is 2 : 1. Find each exterior angle of the polygon
What is the measure of an exterior angle in a regular triangle?Write your answer as an integer or as a decimal rounded to the nearest tenth.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.