Q3 Draw a triangle that satisfies t... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 3: Q3 (page 97)

Draw a triangle that satisfies the conditions stated. If no triangle can satisfy the conditions, write not possible.
A triangle with two acute exterior angles.

Short Answer

Expert verified

Not possible

Step by step solution

Step 1. Description of step.

An acute angle is an angle which has measure less than $90 掳$ and an obtuse angle is an angle which has measure greater than $90 掳$ .

Step 2. Description of step.

As, the sum of the interior angle and exterior angle of the triangle is $180 掳$ .

If the exterior angle of the triangle is acute that is less than $90 掳$ then the interior angle of the triangle will be obtuse that is greater than $90 掳$ .

As, the two exterior angles of the triangle are acute therefore the two interior angles of the triangle are obtuse.

In the triangle, only one of the interior angle can be obtuse.

As here two of the interior angles of the triangle are obtuse, therefore no such triangle is possible.

Step 3. Draw a triangle that satisfies the condition stated.

If the two exterior angles of the triangle are acute then the two interior angles of the triangle are obtuse and in any triangle only one of the interior angle can be obtuse.

Therefore, no such triangle is possible which has two acute exterior angles.