Question

Pleaseee help with numbers 16 and 17 it would help a lot.

Answer 1

Question 16 ) x = 25 { for an Isosceles Triangle}

Question 16 ) x = 15 { for an Equilateral Triangle}

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

∴
`x = (175)/(7)\\\\x=25`

∴ 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

\
`\therefore x = (45)/(3) \\\therefore x = 15\\`

∴ x = 15 .......for QS no. 17