Exercise 34 Page 159

Practice makes perfect

Examining the diagram, we see that the triangle is an equilateral triangle. Such a triangle has three congruent angles of 180^(∘)3=60^(∘). With this, we can write an equation.

4x-12^(∘)=60^(∘) Let's solve this equation.

4x-12^(∘)=60^(∘)

SubEqn

LHS-12^(∘)=RHS-12^(∘)

4x=48^(∘)

DivEqn

.LHS /4.=.RHS /4.

x=12^(∘)

Since this is a right triangle, we can solve for x by using the Pythagorean Theorem.

a^2+b^2=c^2

SubstituteValues

Substitute values

3.1^2+x^2=4.9^2

▼

Solve for x

CalcPow

Calculate power

9.61+x^2=24.01

SubEqn

LHS-9.61=RHS-9.61

x^2=14.4

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=± 3.79473...

x > 0

x= 3.79473...

RoundDec

Round to 1 decimal place(s)

x≈ 3.8

First, we will label some angles and vertices of the figure.

Examining the diagram, we can identify two triangles, △ ABC and △ BCD. In △ ABC, we know two of the three angles. By the Triangle Sum Theorem, the sum of a triangle's angle measures equals 180^(∘). With this, we can find the measure of z.

z+103^(∘)+51^(∘)=180^(∘)

AddTerms

Add terms

z+154^(∘)=180^(∘)

SubEqn

LHS-154^(∘)=RHS-154^(∘)

x=26^(∘)

Note that z and y are alternate interior angles and, since AB ∥ DC, we know these angles are congruent by the Alternate Interior Angles Theorem.