Question

in exercises 7–10, find the value of x. (see example 2.)
7.

a
/ \\
b---c
x 12
8.

m
/ \\
l---n
x 60° 60° 16
9.

s
/ \\
r---t
x°
10.

e
/ \\
d---f
5 3x° 5 5

Explanation:

Problem 7:

Step1: Identify triangle type

Triangle \(ABC\) has \(\angle B=\angle C\), so it's isosceles with \(AB = AC\).

Step2: Determine \(x\)

Given \(AC = 12\), so \(AB=x = 12\).

Step1: Find third angle

In \(\triangle MLN\), angles sum to \(180^\circ\). \(\angle M=180 - 60 - 60=60^\circ\).

Step2: Identify triangle type

All angles \(60^\circ\), so equilateral. Thus \(x = LN = 16\).

Step1: Identify triangle type

Triangle \(RST\) has all sides equal (marked congruent), so equilateral.

Step2: Find angle measure

Each angle in equilateral triangle is \(60^\circ\), so \(x = 60\).

Answer:

\(x = 12\)

Problem 8: