Question

Suppose that ABCD is isosceles with base CB.

Suppose also that m/C=(2x+44) and mZD= (3x+43)°.
Find the degree measure of each angle in the triangle.

Answer 1

• B = C = 58°
• D = 64°

Explanation:

You want to know the measures of angles in isosceles ∆BCD with base CB and angles C=2x+44 and D=3x+43.

Angle sum theorem

The sum of angles in a triangle is 180°. Angles at the ends of the base (CB) are congruent. This lets us write an equation for the angle measures.

∠B + ∠C + ∠D = 180

(2x +44) +(2x +44) +(3x +43) = 180 . . . . ∠C = ∠B

Solution

Simplifying the equation, we have ...

7x +131 = 180

7x = 49

x = 7

(2x +44) = 2(7) +44 = 58

(3x +43) = 3(7) +43 = 64

The measures of the angles are ...

• B = C = 58°
• D = 64°