Question

Ssignment

Answer 1

Part a: The value of x is 33°

Part b: The measure of each base angle is 69°

Explanation:

It is given that the vertex angle of an isosceles triangle measures 42°.

The base angle in the triangle has a measure of $(2x+3)^{\circ}$

Part a: To determine the value of x

Since, in an isosceles triangle the base angles are always equal.

Thus, the three angles in an isosceles triangle add up to 180°

Hence, we have,

$42+2x+3+2x+3=180$

              $42+4x+6=180$

                     $4x+48=180$

                             $4x=132$

                               $x=33^{\circ}$

Thus, the value of x is 33°

Part b: To find the measure of each base angle.

Base angle = $(2 x+3)^{\circ}$

Substituting $x=33^{\circ}$ , we get,

$Base \ angle = (2(33)+3)^{\circ}$

                  $=(66+3)^{\circ}$

                  $=69^{\circ}$

Thus, the measure of each base angle is 69°