Exercise 10 Page 243

Let's analyze the given diagram, where △ MNP ≅ △ TUS.

To find the values of x and y, we will use the fact that corresponding angles have equal measures and corresponding sides have equal lengths. Before we attempt to create a system of equations to solve for x and y, we can use the Triangle Angle-Sum Theorem to find the measure of the remaining angle in △ MNP. 142^(∘)+m∠ N+24^(∘)=180^(∘) Let's solve this equation.

142+m∠ N +24 = 180

AddTerms

Add terms

166+m∠ N = 180

SubEqn

LHS-166=RHS-166

m∠ N = 14

Now we know the measures of all the angles in △ MNP. From the given congruence statement, we know that ∠ N≅ ∠ U and NP≅ SU. This means that we can equate their measures. 2x-50=14 2x-y=13 Since the first equation contains one variable, let's solve it first.

2x-50=14 & (I) 2x-y=13 & (II)

▼

(I): Solve for x

AddEqn

(I): LHS+50=RHS+50

2x=64 2x-y=13

DivEqn

(I): .LHS /2.=.RHS /2.

x=32 2x-y=13

We found that x=32, let's substitute it to the second equation to find the value of y.

x=32 2x-y=13

Substitute

(II): x= 32

x=32 2( 32)-y=13

▼

(II): Solve for y

Multiply

(II): Multiply

x=32 64-y=13

SubEqn

(II): LHS-64=RHS-64

x=32 - y=-51

DivEqn

(II): .LHS /(-1).=.RHS /(-1).

x=32 y=51