1. If a vertex angle of an isosceles triangle is 50. How many degrees is the vertex angle?

2. A base angle if an isosceles triangle is 48, how many degrees is the vertex angle?

3. If a right triangle is isosceles, what is the measure of each acute angle?

4. Can an isosceles triangle be an acute triangle? Why?

5. If a triangle equiangular , how many degrees is each angle?

6. In ∆ XYZ,
7. The angles of a triangle are in ratio of 3:4:5. Find the measure of all the angles.

8. The smallest angle of triangle is 5 times the largest angle. The other angle is five times the smallest. Find the measure of all angles.

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In question number 1, i think we're looking for the base angle, because vertex angle is given at 50 degrees.
Number 6 is not complete.  Number 8 does not make sense. How can the smallest angle be 5 times the largest angle, and the angle between them (medium) has the biggest measurement of them all?

Answers

  • Brainly User
2016-02-17T13:42:42+08:00
1)  If the measure of vertex angle is given, solve for the base angle.
      Base angle = (180 - vertex angle) ÷ 2
                         = (180 - 50) ÷ 2
                         = 130 ÷ 2
                         = 65° 

2)  vertex angle = 180 - 2(base angle)
                         = 180 - 2 (48)
                         = 180 - 96
                         = 84°

3) Base angle = (180 - 90) ÷ 2
                         = 90 ÷ 2
                         = 45°
    Each acute angle is 45°.

4)  Yes. Items Number 1 and 2 are examples of acute isosceles triangles.       Each angle measure less than 90°.
      The measurement of angles in acute isosceles triangle in Number 1 is 65°-50°-65°.  (65 + 50 + 65 = 180°)
      The measurement of angles in acute isosceles triangle in Number 2 is 48° - 84° - 48°.(48 + 84 + 48 = 180°)

5)  An equiangular triangle has 60°-60°-60° angles.

6)  (The question is not complete.)

7)  3x + 4x + 5x = 180
     12x = 180
     12x / 12 = 180 / 12
      x = 15
  
     Substitute 15 for x:
      3 (15) = 45°
      4 (15) = 60°
      5 (15) = 75°
   
     The angles measure 45°, 60°, 75°.
     (45 + 60 + 75 = 180°)

8)  It does not make sense that the smallest angle is 5 times the largest number.


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