Math

QuestionIn triangle MAT\triangle M A T, find mMATm \angle MAT given mMHA=(6y6)m \angle MHA=(6y-6)^{\circ} and mMAT=(3y7)m \angle MAT=(3y-7)^{\circ}.

Studdy Solution

STEP 1

Assumptions1. MH\overline{MH} is the altitude of MAT\triangle MAT. . mMHA=(6y6)m \angle MHA = (6y-6)^\circ.
3. mMAT=(3y7)m \angle MAT = (3y-7)^\circ.
4. An altitude intersects the base of a triangle at 9090^\circ.

STEP 2

We know that MH\overline{MH} is the altitude of MAT\triangle MAT. Therefore, MHA\angle MHA is a right angle, which means it measures 9090^\circ. We can set the measure of MHA\angle MHA equal to 9090^\circ and solve for yy.
6y6=906y-6=90

STEP 3

Add6 to both sides of the equation to isolate the term with yy.
6y=90+66y =90 +6

STEP 4

Calculate the right side of the equation.
6y=966y =96

STEP 5

Divide both sides of the equation by to solve for yy.
y=96y = \frac{96}{}

STEP 6

Calculate the value of yy.
y=16y =16

STEP 7

Now that we have the value of yy, we can substitute it into the expression for mMATm \angle MAT to find the measure of this angle.
mMAT=3y7m \angle MAT =3y -7

STEP 8

Substitute y=16y =16 into the equation.
mMAT=3(16)7m \angle MAT =3(16) -7

STEP 9

Calculate the value of mMATm \angle MAT.
mMAT=487=41m \angle MAT =48 -7 =41^\circSo, the measure of MAT\angle MAT is 4141^\circ.

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