Question

In the triangle below, ZC is a right angle. Suppose that m Z B=(2x+43)° and m Z D= (5x+5)°.

(a) Write an equation to find x. Make sure you use an "=" sign in your
D
(5x +5)
(2x+43)
Equation:
(b) Find the degree measure of each angle.
mZB=
m2c=
mZD=
0=0
X

Answer 1

a) 7x + 48 = 90 which simplifies to 7x = 42

b) m∠B = 35°m m∠C = 90°, m∠D = 55°

Explanation:

The three angles of a triangle add up to 180°

Therefore the sum of the measures of angles B, C and D should be 180

==> m∠B + m∠C + m∠d = 180

Since m∠C = 90,

m∠B + 90 + m∠D = 180

m∠B + m∠D = 180 - 90 = 90

Since m∠B = (2x+43)° and m∠D = (5x+5)°.

(2x + 43) + (5x + 5) = 90

==> 7x + 48 = 90

==> 7x = 90 - 48 = 42

==> x = 42/7 = 6

b)

m∠B = 5 x 6 + 5 = 35°

m∠C = 90°

m∠D = 2 x 6 + 43 = 12 + 43 = 55°