Question

1. what is the value of x?

f. x = 10
g. x = 15
h. x = 25
j. x = 50

1. given that △abc ≅ △def, m∠c = (x)° and m∠f = (4x - 75)°

find the angle measurements for angles c and f.
f. 25°
g. 50°
h. 5°
j. 10°

1. find the value of x.

Explanation:

Question 8

Step1: Use the exterior angle theorem

The exterior angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, \(2x\) is an exterior angle of the triangle with interior angles \(20^{\circ}\) and \(30^{\circ}\). So, \(2x=20 + 30\).

Step2: Solve for \(x\)

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Step1: Use the property of congruent triangles

Since \(\triangle ABC\cong\triangle DEF\), then \(\angle C\cong\angle F\). So, \(m\angle C=m\angle F\), which gives the equation \(x = 4x-75\).

Step2: Solve the equation for \(x\)

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Step1: Use the property of an isosceles triangle

The triangle is isosceles (two sides are equal), so the base angles are equal. The exterior angle \(3(x + 7)\) is equal to the sum of the two non - adjacent interior angles. Let the two non - adjacent interior angles be \(y\) and \(63^{\circ}\). Also, since the triangle is isosceles, \(y = 63^{\circ}\). Then \(3(x + 7)=63+63\).

Step2: Simplify the right - hand side

\(3(x + 7)=126\)

Step3: Divide both sides by 3

\(x + 7=\frac{126}{3}=42\)

Step4: Solve for \(x\)

\(x=42 - 7=35\)

Answer:

H. \(x = 25\)

Question 10