Answer:
Question 16 ) x = 25 { for an Isosceles Triangle}
Question 16 ) x = 15 { for an Equilateral Triangle}
Step-by-step explanation:
Question 16 )
Solution:
The given Triangle is an Isosceles triangle because two sides are equal that is five unit and five unit.
Another property for an Isosceles triangle is base angles are equal.
∴ one of the base angle is given ( 2x + 3 )°,so other will be also the same that is ( 2x + 3 )° i.e m∠B = m∠ C = ( 2x + 3 )°.
m∠ A=(3x -1 )°
We have drawn in the diagram and label the diagram as Δ ABC
We know that property for the Triangle SUM of the measures of the angle of a triangle is 180°.
∴ m∠ A + m∠ B + m∠ C = 180° ...{Angle sum property of a triangle}
∴ (3x - 1) + (2x+ 3) + (2x+3) = 180°
∴ 7x + 5 + 180
∴ 7x = 175
∴ [tex]x = \frac{175}{7}\\\\x=25[/tex]
∴ x = 25 .........QS no. 16
Question 17 )
Solution:
We have an equilateral triangle Δ ABC and measure of each angle is ( 3x +15 )°
We know that all the angles of an equilateral triangle are equal and measure of each angle of an equilateral triangle is 60°.
∴ m∠ A = m∠ B = m∠ C = (3x+ 15)° = 60°
∴ 3x + 15 = 60
∴ 3x = 45
\[tex]\therefore x = \frac{45}{3} \\\therefore x = 15\\[/tex]
∴ x = 15 .......for QS no. 17
