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A straightforward way to see what \(x\) must be is to notice that the angles \(63^\circ\) and \((15x - 3)^\circ\) sit on a straight line at the top (they form a linear pair). Linear‐pair angles sum to \(180^\circ\). So: \[ 63^\circ + (15x - 3)^\circ \;=\; 180^\circ \quad\Longrightarrow\quad 15x + 60 \;=\; 180 \quad\Longrightarrow\quad 15x \;=\; 120 \quad\Longrightarrow\quad x \;=\; 8. \] Once you have \(x = 8\), plug that into the other expression \((8x + 7)^\circ\): \[ 8x + 7 \;=\; 8\cdot 8 + 7 \;=\; 64 + 7 \;=\; 71. \] In the diagram, angle \(1\) and the angle labeled \((8x + 7)^\circ\) are **vertical angles** (i.e., they’re across from each other at the intersection on line \(m\)). Vertical angles are **congruent**, so \[ m\angle 1 \;=\; (8x + 7)^\circ \;=\; 71^\circ. \] Hence the measure of angle \(1\) is \(\boxed{71^\circ}.\)
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Sat, 11 Jan 2025 02:28 GMT